Math 2 5.1.3
Find the solutions to the equation below: 16x²-64=0
16x² and 64 are both perfect squares: they break down into 4x+8=0 and 4x-8=0. Solve those two smaller equations to find the correct answers (there are 2).
Find the solutions to the equation below: 25x²-100=0
25x² and 100 are both perfect squares: they break down into 5x+10=0 and 5x-10=0. Solve those two smaller equations to find the correct answers (there are 2).
Find the solutions to the equation: 9x²-81=0
9x² and 81 are both perfect squares: they break down into 3x+9=0 and 3x-9=0. Solve those two smaller equations to find the correct answers (there are 2).
True or False: A quadratic equation in standard form is written ax² + bx = c, where a, b, and c are real numbers and a is not zero.
False
True or False: A quadratic equation in standard form is written ax² = bx + c, where a, b, and c are real numbers and a is not zero.
False
Find ALL solutions to: x² + 4x - 9 = 5x + 3
Step 1: move the 5x+3 to the other side by subtracting both terms x² - x - 12 =0 Step 2: Factor - what two numbers that multiply together to make -12 can be subtracted to make -1? That would be -4 and 3, therefore: (x-4)(x+3)=0 Step 3: Set up each small equation against 0 and solve: x-4=0; x=? x+3=0; x=?
Find ALL solutions to: x² + 4x - 9 = x + 1
Step 1: move the x+1 to the other side by subtracting both terms x² + 3x - 10 =0 Step 2: Factor - what two numbers that multiply together to make -10 can be subtracted to make 3? That would be 5 and -2, therefore: (x+5)(x-2)=0 Step 3: Set up each small equation against 0 and solve: x+5=0; x=? x-2=0; x=?
Write the following equation in the form ax² + bx + c = 0: x+10=3(x-1)²
Step 1: square (x-1) x+10=3(x²-2x+1) Step 2: distribute the 3 x+10=3x²-6x+3 Step 10: move everything to 1 side. It is easiest to subtract the x and the 9 from the left side and then move the 0 to the other side: 3x²-(6x-x)+(2-10)=0
Write the following equation in the form ax² + bx + c = 0: x+9=2(x-1)²
Step 1: square (x-1) x+9=2(x²-2x+1) Step 2: distribute the 2 x+9=2x²-4x+2 Step 3: move everything to 1 side. It is easiest to subtract the x and the 9 from the left side and then move the 0 to the other side: 2x²-(4x-x)+(2-9)=0
Write the following equation in the form ax² + bx + c = 0: x+9=4(x-1)²
Step 1: square (x-1) x+9=4(x²-2x+1) Step 2: distribute the 4 x+9=4x²-8x+4 Step 3: move everything to 1 side. It is easiest to subtract the x and the 9 from the left side and then move the 0 to the other side: 2x²-(8x-x)+(4-9)=0
Find ALL solutions to: x² + 6x + 9 = 20
This is a perfect square trinomial. Step 1: Take the square root of both sides: x+3 = √20 Step 2: Factor the √20 into √5 and √4. √4=2 OR -2 x+3 = 2√5 OR x+3 = - 2√5 Step 3: Solve both equations by subtracting 3 from both sides x=2√5 -3 OR x= - 2√5-3
Find ALL solutions to: x² + 10x + 25 = 8
This is a perfect square trinomial. Step 1: Take the square root of both sides: x+5 = √8 Step 2: Factor the √8 into √2 and √4. √4=2 OR -2 x+5 = 2√2 OR x+5 = - 2√2 Step 3: Solve both equations by subtracting 5 from both sides x=2√2 -5 OR x= - 2√2-5
Write the following equation in the form ax² + bx + c = 0: x²+8x+10=3
To solve, move the 3 to the other side by SUBTRACTING it from 10
Write the following equation in the form ax² + bx + c = 0: x²+6x+8=3
To solve, move the 3 to the other side by SUBTRACTING it from 8
Write the following equation in the form ax² + bx + c = 0: x²+7x+9=3
To solve, move the 3 to the other side by SUBTRACTING it from 9
True or False: A quadratic equation in standard form is written ax² + bx + c = 0, where a, b, and c are real numbers and a is not zero.
True
A student performed the following steps to find the solution to the equation x²-2x-8=0. Where did the student go wrong? Step 1. Factor the polynomial into (x - 4) and (x - 2) Step 2. x - 4 = 0 and x - 2 = 0 Step 3. x = 4 and x = 2
in Step 1: these are the wrong factors. The -8 in the equation shows that one factor will be positive and one will be negative
A student performed the following steps to find the solution to the equation x²+4x-12=0. Where did the student go wrong? Step 1. Factor the polynomial into (x + 6) and (x - 2) Step 2. x - 6 = 0 and x + 2 = 0 Step 3. x = 6 and x = -2
in Step 2: they reversed the signs
A student performed the following steps to find the solution to the equation x²-2x-15=0. Where did the student go wrong? Step 1. Factor the polynomial into (x + 3) and (x - 5) Step 2. x + 3 = 0 and x - 5 = 0 Step 3. x = 3 and x = -5
in Step 3: they did not change the signs due to subtracting the 3 and adding the 5
Find ALL solutions to: (2x+3)² = 10
Step 1: Take the square root of both sides 2x+3=√10 Step 2: subtract 3 from both sides 2x=√10-3 Step 3: Divide by 2 on both sides x=√10-3/2 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: (3x + 4)² = 14
Step 1: Take the square root of both sides 3x+4=√14 Step 2: subtract 1 from both sides 3x=√14-4 Step 3: Divide by 5 on both sides x=√14-4/3 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: (3x - 5)² = 19
Step 1: Take the square root of both sides 3x-5=√19 Step 2: add 5 to both sides 3x=√19 +5 Step 3: Divide by 3 on both sides x=√19+5/3 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: (4x - 1)² = 11
Step 1: Take the square root of both sides 4x-1=√11 Step 2: add 1 to both sides 4x=√11 +1 Step 3: Divide by 4 on both sides x=√11+1/4 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: (5x + 1)² = 7
Step 1: Take the square root of both sides 5x+1=√7 Step 2: subtract 1 from both sides 5x=√7-1 Step 3: Divide by 5 on both sides x=√7-3/5 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: (5x - 2)² = 10
Step 1: Take the square root of both sides 5x-2=√10 Step 2: add 2 to both sides 5x=√10 +2 Step 3: Divide by 5 on both sides x=√10+2/5 Remember that you will have one positive answer and one negative answer
Find ALL solutions to: x² + 5x - 8 = 4x + 4
Step 1: move the 4x+4 to the other side by subtracting both terms x² + x - 12 =0 Step 2: Factor - what two numbers that multiply together to make -12 can be subtracted to make 1? That would be 4 and -3, therefore: (x+4)(x-3)=0 Step 3: Set up each small equation against 0 and solve: x+4=0; x=? x-3=0; x=?
Find ALL solutions to: 4x² + 4x + 1 = 9
This is a perfect square trinomial. Step 1: Take the square root of both sides: 2x+1=3 OR 2x+1= -3 Step 2: Subtract 1 from both sides of both equations 2x=2 OR 2x= -4 Step 3: Solve by dividing by 2 x=1 OR x= -2
Find ALL solutions to: 4x²+ 12x + 9 = 25
This is a perfect square trinomial. Step 1: Take the square root of both sides: 2x+3=5 OR 2x+3= -5 Step 2: Subtract 5 from both sides of both equations 2x=2 OR 2x= -8 Step 3: Solve by dividing by 2 x=1 OR x= -4
Find ALL solutions to: 4x²+ 20x + 25 = 49
This is a perfect square trinomial. Step 1: Take the square root of both sides: 2x+5=7 OR 2x+5= -7 Step 2: Subtract 5 from both sides of both equations 2x=2 OR 2x= -12 Step 3: Solve by dividing by 2 x=1 OR x= -6
Find ALL solutions to: x² + 4x + 4 = 12
This is a perfect square trinomial. Step 1: Take the square root of both sides: x+2 = √12 Step 2: Factor the √12 into √3 and √4. √4=2 OR -2 x+2 = 2√3 OR x+2 = - 2√3 Step 3: Solve both equations by subtracting 2 from both sides x=2√3 -2 OR x= -2√3-2