1105 ALGEBRA I (PACE)
JOB 11:18
And thou shalt be secure, because there is hope; yea, thou shalt dig about thee, and thou shalt take thy rest in safety.
SOLVE BY FACTORING. CHECK THE ROOTS. a(a + 5) = 14
a=-7 a=2
SOLVE THE QUADRATIC EQUATION BY FACTORING. CHECK THE ROOTS. c^2 - 5c + 4 = 0
c=4 c=1
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. c^2 - 7c = -12
c=4 c=3
A quadratic equation with the second power of the unknown, but not the first power, is called a/an __________ quadratic equation.
incomplete
A quadratic equation is an equation that has the __________ power, but no higher power of the unknown.
second
Most quadratic equations have __________ roots.
two
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. (x^2/2) + 2x + 3/2 = 0
x=-1 x=-3
SOLVE BY FACTORING. CHECK THE ROOTS. x = (10/x - 3)
x=-2 x=5
STATE THIS WORD PROBLEM AS A QUADRATIC EQUATION. SOLVE AND CHECK. If the square of a positive number is increased by 3 times the number, the result is 54. Find the number.
x=-9 (Incorrect solution, because the number is positive) x=6
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. 5x^2 + 4x - 1 = 0
x=1/5 x=-1
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. x^2 - 8x - 20 = 0
x=10 x=-2
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. x^2 - 3 = 118
x=11 x=-11
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTION. 3√(2x) - 26 = -8
x=18
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. x^2 + 3x - 10 = 0
x=2 x=-5
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTIONS. √x - 3 = 2
x=25
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTIONS. √(x/4) = 8
x=256
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. 4x^2 = 160
x=2√10 x=-2√10
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. x/10 = 6/x
x=2√15 x=-2√15
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. x^2 = 2x + 3
x=3 x=-1
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. 3x^2 - 8x = 3
x=3 x=-1/3
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. 2x^2 - 2 = 16
x=3 x=-3
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. x^2 - x = 3/4
x=3/2 x=-1/2
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. 2x^2 + 3x = 9
x=3/2 x=-3
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTIONS. 2√(4x) - 6 = 18
x=36
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. x^2 - 2x - 8 = 0
x=4 x=-2
SOLVE BY USING THE QUADRATIC FORMULA. CHECK THE ROOTS. 3x^2 + 8 = 14x
x=4 x=2/3
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTION. 3√x = 2
x=4/9
SOLVE THE QUADRATIC EQUATION BY FACTORING. CHECK THE ROOTS. 4/x + 8 = 2x - 6/x
x=5 x=-1
SOLVE BY COMPLETING THE SQUARE. CHECK THE ROOTS. 2x^2 - 9x - 5 = 0
x=5 x=-1/2
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTIONS. 4√(2x-1) = 8
x=5/2
SOLVE THE QUADRATIC EQUATION BY FACTORING. CHECK THE ROOTS. x^2 - 10x = -24
x=6 x=4
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. x/9 = 8/x
x=6√2 x=-6√2
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTION. √(x/5) = 12
x=720
STATE THE WORD PROBLEM AS A QUADRATIC EQUATION. SOLVE AND CHECK. The difference between two positive numbers is 5. Their product is 104. Find the numbers.
x=8 (smaller number) x+5=13 (larger number)
SOLVE THE INCOMPLETE QUADRATIC EQUATION. CHECK THE ROOTS. x^2 - 71 = 10
x=9 x=-9
SOLVE BY FACTORING. CHECK THE ROOTS. 3y^2 - 10y - 8 = 0
y=-2/3 y=4
SOLVE THE RADICAL EQUATION. CHECK YOUR SOLUTION. √(5y - 1) = 7
y=10
