Question

Solve the quadratic equation by completing the square.
x²–2x-12=0

Answer 1

`(x-1)^2-13=0`

`x = √(13)+1`

Explanation:

Completing the square is a method of rewriting a quadratic equation in the standard form such that it is in vertex form. The first step is to group the linear and quadratic terms, then factor out the coefficient of the quadratic term. After doing so, complete the square, add a value such that the linear and quadratic terms form a perfect square trinomial. Do not forget to balance the equation. The final step is to simplify.

`x^2-2x-12=0`

Group,

`(x^2-2x)-12=0`

Complete the square,

`(x^2-2x+1)-12-1=0`

Simplify,

`(x-1)^2-13=0`

Now solve the equation using inverse operations,

`(x-1)^2-13=0\\\\(x-1)^2=13\\\\x-1=√(13)\\\\x = √(13)+1`