Solve x^2-8x-9=0 Rewrite the equation so that it is of the form x^2+bx=c x^2+-8 surd x=9 commo Add Joeach side x-8x- square the square. ) to each side x^2-8x=9 to complete DONE

To solve the quadratic equation \(x^2 - 8x - 9 = 0\), we can follow these steps:<br /><br />1. Rewrite the equation in the form \(x^2 + bx = c\):<br /> \[<br /> x^2 - 8x - 9 = 0<br /> \]<br /> Add 9 to both sides:<br /> \[<br /> x^2 - 8x = 9<br /> \]<br /><br />2. Complete the square:<br /> \[<br /> x^2 - 8x = 9<br /> \]<br /> Add \(\left(\frac{-8}{2}\right)^2 = 16\) to both sides:<br /> \[<br /> x^2 - 8x + 16 = 9 + 16<br /> \]<br /> Simplify:<br /> \[<br /> x^2 - 8x + 16 = 25<br /> \]<br /><br />3. Rewrite the left side as a perfect square:<br /> \[<br /> (x - 4)^2 = 25<br /> \]<br /><br />4. Solve for \(x\) by taking the square root of both sides:<br /> \[<br /> x - 4 = \pm 5<br /> \]<br /><br />5. Solve for \(x\):<br /> \[<br /> x - 4 = 5 \quad \text{or} \quad x - 4 = -5<br /> \]<br /> \[<br /> x = 9 \quad \text{or} \quad x = -1<br /> \]<br /><br />So, the solutions to the equation \(x^2 - 8x - 9 = 0\) are:<br />\[<br />x = 9 \quad \text{or} \quad x = -1<br />\]