Asked by Smartypants
Solve x2+2x−36=9x+24by factoring
Answers
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Answered by
GPT-4o mini
To solve the equation \(x^2 + 2x - 36 = 9x + 24\) by factoring, follow these steps:
1. **Rearrange the equation** by moving all terms to one side:
\[
x^2 + 2x - 36 - 9x - 24 = 0
\]
Simplifying this gives:
\[
x^2 + 2x - 9x - 36 - 24 = 0
\]
Combine like terms:
\[
x^2 - 7x - 60 = 0
\]
2. **Factor the quadratic**:
We need to factor \(x^2 - 7x - 60\). We are looking for two numbers that multiply to \(-60\) and add to \(-7\). The numbers \(-12\) and \(5\) meet these criteria.
Thus, we can factor the quadratic as:
\[
(x - 12)(x + 5) = 0
\]
3. **Set each factor to zero**:
Now, solve for \(x\) by setting each factor equal to zero:
\[
x - 12 = 0 \quad \Rightarrow \quad x = 12
\]
\[
x + 5 = 0 \quad \Rightarrow \quad x = -5
\]
4. **Final solution**:
The solutions to the equation \(x^2 + 2x - 36 = 9x + 24\) are:
\[
x = 12 \quad \text{and} \quad x = -5.
\]
1. **Rearrange the equation** by moving all terms to one side:
\[
x^2 + 2x - 36 - 9x - 24 = 0
\]
Simplifying this gives:
\[
x^2 + 2x - 9x - 36 - 24 = 0
\]
Combine like terms:
\[
x^2 - 7x - 60 = 0
\]
2. **Factor the quadratic**:
We need to factor \(x^2 - 7x - 60\). We are looking for two numbers that multiply to \(-60\) and add to \(-7\). The numbers \(-12\) and \(5\) meet these criteria.
Thus, we can factor the quadratic as:
\[
(x - 12)(x + 5) = 0
\]
3. **Set each factor to zero**:
Now, solve for \(x\) by setting each factor equal to zero:
\[
x - 12 = 0 \quad \Rightarrow \quad x = 12
\]
\[
x + 5 = 0 \quad \Rightarrow \quad x = -5
\]
4. **Final solution**:
The solutions to the equation \(x^2 + 2x - 36 = 9x + 24\) are:
\[
x = 12 \quad \text{and} \quad x = -5.
\]
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