# Solve this quadratic equation using the following 6 steps: x^2 + 12x - 64 = 0 a) Move the constant term to the right side of the equationb) Multiply each term in the equation by four times the...

Solve this quadratic equation using the following 6 steps:

x^2 + 12x - 64 = 0

a) Move the constant term to the right side of the equation

b) Multiply each term in the equation by four times the coefficient of the x^2 term

c) Square the coeffient of the original x term and add it to both sides of the equation.

d) Take the square root of both sides

e) Set the left side of the equation equal to the positive square root of the number on the right side and solve for x.

f) Set the left side of the equation eual to the negative square root of the number on the right side of the equation and solve for x.

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### 1 Answer

You need to solve the quadratic equation by completing the square.

The first step is to move the constant terms, that is -64, to the right side, such that:

`x^2 + 12x = 64`

You need to complete the square to the left side, hence you need to add 36 both sides such that:

`x^2 + 12x + 36 = 64 + 36`

Notice that expansion to the left side is the square of binomial (x + 6) such that:

`(x+6)^2 = 100`

You need to take square root both sides such that:

`x + 6 = +-sqrt100`

You need to set the left side equal to positive square root of 100 such that:

`x + 6 = 10 =gt x = 10 - 6 =gt x_1=4`

You need to set the left side equal to negative square root of 100 such that:

`x + 6 = -10 =gt x = -10 - 6 =gt x_2=-16`

**Hence, using completion of square method to solve quadratic equation yields`x_1 = 4` and`x_2 = -16` .**