Questions: Solve the following equation. For an equation with a real solution, support your answers graphically.
x^2 - 9x = x - 22
Transcript text: Solve the following equation. For an equation with a real solution, support your answers graphically.
\[
x^{2}-9 x=x-22
\]
Solution
Solution Steps
To solve the equation \(x^2 - 9x = x - 22\), first rearrange it to form a standard quadratic equation. Then, use the quadratic formula to find the real solutions. Finally, plot the quadratic function to visually confirm the solutions.
Step 1: Move All Terms to One Side
The given equation is:
\[
x^2 - 9x = x - 22
\]
First, move all terms to one side of the equation to set it to zero:
\[
x^2 - 9x - x + 22 = 0
\]
Simplify the equation:
\[
x^2 - 10x + 22 = 0
\]
Step 2: Use the Quadratic Formula
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
For the equation \(x^2 - 10x + 22 = 0\), the coefficients are \(a = 1\), \(b = -10\), and \(c = 22\).
Substitute these values into the quadratic formula: