Which equation has the same solution as x, squared, plus, 2, x, minus, 9, equals, minus, 2x

Question

2
+2x−9=−2?
Answer
Attempt 1 out of 3
Multiple Choice Answers
left parenthesis, x, minus, 1, right parenthesis, squared, equals, 6(x−1)
2
=6
left parenthesis, x, minus, 1, right parenthesis, squared, equals, 8(x−1)
2
=8
left parenthesis, x, plus, 1, right parenthesis, squared, equals, 6(x+1)
2
=6
left parenthesis, x, plus, 1, right parenthesis, squared, equals, 8(x+1)
2
=8

Answer 1

To solve \( x^2 + 2x - 9 = -2 \), we first rearrange it:

\[ x^2 + 2x - 9 + 2 = 0 \]

This simplifies to:

\[ x^2 + 2x - 7 = 0 \]

Now we need to find an equation that has the same solution. We can start by rewriting this in a different form.

Next, let's compare the multiple-choice equations given and see if they can be simplified or transformed to match our equation:

1. \( (x - 1)^2 = 6 \)
2. \( (x - 1)^2 = 8 \)
3. \( (x + 1)^2 = 6 \)
4. \( (x + 1)^2 = 8 \)

Analyzing the options:

Let's expand these equations to see how they compare.

1. \( (x - 1)^2 = 6 \):

\[ x^2 - 2x + 1 - 6 = 0 \implies x^2 - 2x - 5 = 0 \]

2. \( (x - 1)^2 = 8 \):

\[ x^2 - 2x + 1 - 8 = 0 \implies x^2 - 2x - 7 = 0 \]

3. \( (x + 1)^2 = 6 \):

\[ x^2 + 2x + 1 - 6 = 0 \implies x^2 + 2x - 5 = 0 \]

4. \( (x + 1)^2 = 8 \):

\[ x^2 + 2x + 1 - 8 = 0 \implies x^2 + 2x - 7 = 0 \]

Conclusion:

After simplifying, we found that:

• Equation 2 \( (x - 1)^2 = 8 \) becomes \( x^2 - 2x - 7 = 0 \), which matches our rearranged equation.
• Equation 4 \( (x + 1)^2 = 8 \) also becomes \( x^2 + 2x - 7 = 0 \).

However, since we want the exact match of \( x^2 + 2x - 7 = 0 \), the correct answer among the choices is:

Answer: \( (x - 1)^2 = 8 \).