Asked by Smartypants
Solve the equation.x squared equals 9 x plus 10Question content area bottomPart 1x =enter your response here(Use a comma to separate answers as needed.)
Answers
Answered by
GPT-4o mini
To solve the equation \( x^2 = 9x + 10 \), we first rearrange it to set it to zero:
\[
x^2 - 9x - 10 = 0
\]
Now we can factor this quadratic equation. We are looking for two numbers that multiply to \(-10\) (the constant term) and add to \(-9\) (the coefficient of \(x\)).
The numbers that satisfy these conditions are \(-10\) and \(1\), since:
\[
-10 \times 1 = -10 \\
-10 + 1 = -9
\]
Now we can rewrite and factor the quadratic:
\[
(x - 10)(x + 1) = 0
\]
Setting each factor to zero gives us the solutions:
1. \(x - 10 = 0 \) → \( x = 10 \)
2. \(x + 1 = 0 \) → \( x = -1 \)
Therefore, the solutions to the equation \( x^2 = 9x + 10 \) are:
\[
x = 10, -1
\]
So the answer is:
\[
10, -1
\]
\[
x^2 - 9x - 10 = 0
\]
Now we can factor this quadratic equation. We are looking for two numbers that multiply to \(-10\) (the constant term) and add to \(-9\) (the coefficient of \(x\)).
The numbers that satisfy these conditions are \(-10\) and \(1\), since:
\[
-10 \times 1 = -10 \\
-10 + 1 = -9
\]
Now we can rewrite and factor the quadratic:
\[
(x - 10)(x + 1) = 0
\]
Setting each factor to zero gives us the solutions:
1. \(x - 10 = 0 \) → \( x = 10 \)
2. \(x + 1 = 0 \) → \( x = -1 \)
Therefore, the solutions to the equation \( x^2 = 9x + 10 \) are:
\[
x = 10, -1
\]
So the answer is:
\[
10, -1
\]
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