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

Answer:

B.(4,20)

Step-by-step 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

$-\dfrac{24}{2}=-12$

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

$x-12=\pm \sqrt{64}$

Step 6: Solve for x

$x=12\pm \sqrt{64}\\=12\pm8\\x=12+8 or x=12-8\\x=20 or x=4.$

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