Question

-2x = x² - 6

1. rewrite the equation by completing the square.

your equation should look like (x + c)² = d or (x - c)² = d.

1. what are the solutions to the equation?

choose 1 answer:
a ( x = 1 pm sqrt{7} )
b ( x = -1 pm sqrt{7} )

Explanation:

Part 1: Rewrite by Completing the Square

Step1: Rearrange the equation

First, we start with the given equation \(-2x = x^2 - 6\). Let's rearrange it to the standard quadratic form \(x^2 + bx = c\).
Adding \(2x\) to both sides and adding \(6\) to both sides, we get:
\(x^2 + 2x = 6\)

Step2: Complete the square

To complete the square for the quadratic expression \(x^2 + 2x\), we take half of the coefficient of \(x\), which is \(\frac{2}{2} = 1\), and then square it: \(1^2 = 1\).
We add this square to both sides of the equation:
\(x^2 + 2x + 1 = 6 + 1\)

Step3: Rewrite as a square

The left - hand side is now a perfect square trinomial, which can be written as \((x + 1)^2\). The right - hand side is \(7\). So the equation becomes:
\((x + 1)^2 = 7\)

Part 2: Find the solutions

Step1: Take the square root of both sides

Starting with the equation \((x + 1)^2 = 7\), we take the square root of both sides. Remember that when we take the square root of a number, we have two solutions (positive and negative). So we get:
\(x + 1=\pm\sqrt{7}\)

Step2: Solve for \(x\)

Subtract \(1\) from both sides of the equation \(x + 1=\pm\sqrt{7}\) to isolate \(x\). We have:
\(x=-1\pm\sqrt{7}\)

Part 1 Answer: \((x + 1)^2 = 7\)

Part 2 Answer: B. \(x=-1\pm\sqrt{7}\)

Answer:

Step1: Take the square root of both sides

Starting with the equation \((x + 1)^2 = 7\), we take the square root of both sides. Remember that when we take the square root of a number, we have two solutions (positive and negative). So we get:
\(x + 1=\pm\sqrt{7}\)

Step2: Solve for \(x\)

Subtract \(1\) from both sides of the equation \(x + 1=\pm\sqrt{7}\) to isolate \(x\). We have:
\(x=-1\pm\sqrt{7}\)

Part 1 Answer: \((x + 1)^2 = 7\)

Part 2 Answer: B. \(x=-1\pm\sqrt{7}\)