Question

jamal solved the equation by completing the square.
x² - 8x + 14 = 0
which equations shows one of the steps jamal could have taken to complete
the square?
○ x² - 8x + 16 = -14 + 16
○ x² - 8x + 64 = -14 + 64
○ x² - 8x + 16 = -14
○ x² - 8x + 64 = -14 + 16

Explanation:

Step1: Recall completing the square

For \(ax^2 + bx + c = 0\), to complete the square, we take half of \(b\), square it, and add/subtract. Here, equation is \(x^2 - 8x + 14 = 0\), so \(x^2 - 8x = -14\). Half of \(-8\) is \(-4\), square is \(16\).

Step2: Add 16 to both sides

Add \(16\) to both sides of \(x^2 - 8x = -14\), get \(x^2 - 8x + 16 = -14 + 16\).

Answer:

A. \(x^2 - 8x + 16 = -14 + 16\)