Question

Solve x^2 -24 = -80 by completing the square.

What is the solution set of the equation?


A.(2,40)


B.(4,20)


C.(5,16)


D.(8,10)

Answer 1

B.(4,20)

Explanation:

Given:
`x^2 -24x = -80`

To solve the quadratic equation by completing the square, we follow these steps.

Step 1: Divide the coefficient of x by 2

`-(24)/(2)=-12`

Step 2: Square your result fro Step 1

`(-12)^2`

Step 3: Add the result form step 2 to both sides of the equation

`x^2 -24x+(-12)^2 = -80+(-12)^2`

Step 4: Rewrite the Left hand side in the form
`(x+k)^2`

`(x-12)^2=-80+144\\(x-12)^2=64`

Step 5: Take square roots of both sides

`x-12=\pm √(64)`

Step 6: Solve for x

`x=12\pm √(64)\\=12\pm8\\x=12+8$ or x=12-8\\x=20 or x=4.`

Therefore, the solution set of the equation is (4,20).