Answer:
d.) x2+16x+64=36
Explanation:
To find - Alicia is solving a quadratic equation. She wants to find the value of x by taking the square root of both sides of the equation. Which equation allows her to do this?
a.) x2+81x+18=54
b.) x2−8x+24=17
c.) x2+9x−24=25
d.) x2+16x+64=36
Proof -
The correct answer is - d.) x2+16x+64=36
x2+16x+64=36
⇒x² + 8x + 8x + 64 = 36
⇒x(x + 8) + 8(x + 8) = 36
⇒(x+8)(x+8) = 36
⇒(x+8)² = 36
Take square root both sides, we get
√(x+8)² = √36
⇒x + 8 = ± 6
⇒x + 8 = 6, x + 8 = -6
⇒x = 6 - 8 , x = -6 - 8
⇒x = -2, -14
So,
Equation (4) allows her to do the following thing she ants.