Pure Maths 2.2 - Completing the square

Complete the square for these expressions: 1. x^2 +8x 2. x^2 - 3x 3. 2x^2 -12x

1 --> (x + 4)^2 - 4^2 = (x + 4)^2 + 16 2 --> (x - 3/2)^2 - 9/4 3 --> 2(x^2 - 6x) - take out a factor of 2 so that you can apply the formula. 2((x - 3)^2 -3^2) = 2(x - 3)^2 - 18 (multiply the outer bracket).

Write 3x^2 + 6x + 1 in the form p(x + q)^2 + r, where p, q and r are integers to be found.

Just use the formula, x^2 + bx = (x + b/2)^2 - (b/2)^2. You should get p = 3, q = 1 and r = -2.

Solve the equation 2x^2 - 8x + 7 = 0. Give your answers in surd form.

Remember to take out a factor of 2 and then use the normal 'completing the square' format. x^2 + bx = (x + b/2)^2 - (b/2)^2. The answer is x = 2 +- 1/√2.

Solve the equation x^2 + 8x + 10 = 0 by completing the square. Give your answers in surd form.

When you are solving with 'completing the square' you basically just wanna make it equal x. 1. (x + 4)^2 - 16 = - 10 2. (x + 4)^2 = 6 3. x + 4 = +-√6 4. x = -4 +-√6

What is the general formula for completing the square?

x^2 + bx = (x + b/2)^2 - (b/2)^2