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.)

Answer 1

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:

\[ 10, -1 \]