Solve $x^2+8x-9=0$

Step-by-step solution

1. Step 1 · Move the constant
   $$x^2+8x=9$$

   Add 9 to both sides.

2. Step 2 · Complete the square
   $$x^2+8x+16=25\Rightarrow (x+4{)}^2=25$$

   Half of 8 is 4, and its square is 16. Add it to both sides.

3. Step 3 · Take both square roots
   $$x+4=\pm 5\Rightarrow x=1\text{ or }-9$$

   Both signs are needed. Substitution gives 1 + 8 − 9 = 0 and 81 − 72 − 9 = 0.