Question

question 6 of 10
what equation results from completing the square and then factoring?
x² - 10x = 46

a. (x - 5)² = 71
b. (x - 10)² = 71
c. (x - 10)² = 21
d. (x - 5)² = 21

Explanation:

Step1: Identify the coefficient of x

The equation is \(x^2 - 10x = 46\). The coefficient of \(x\) is \(-10\).

Step2: Complete the square

To complete the square, take half of the coefficient of \(x\), square it, and add it to both sides. Half of \(-10\) is \(-5\), and squaring it gives \((-5)^2 = 25\). Add 25 to both sides:
\(x^2 - 10x + 25 = 46 + 25\)

Step3: Factor the left side

The left side \(x^2 - 10x + 25\) is a perfect square trinomial, which factors as \((x - 5)^2\). The right side is \(46 + 25 = 71\). So the equation becomes \((x - 5)^2 = 71\).

Answer:

A. \((x - 5)^2 = 71\)