Step 1: Divide all terms by a (the coefficient of x2). In our case, it is 1. So it will not change anything.
Step 2: Move the number term (c/a) to the right side of the equation. In our case, it is 21. Therefore, we have:
[tex]x^2\text{ + 15x = - 21}[/tex]Step 3: Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation, this way:
[tex](\frac{15}{2})^2=7.5^2\text{ = 56.25 }\Rightarrow x^2\text{ + 15x + 56.25 = -21 + 56.25}[/tex]Step 4: Take the square root on both sides of the equation, as follows:
[tex]\sqrt{(x^2\text{ + 15x + 56.25 }}=\text{ }\sqrt{35.25}[/tex][tex]x\text{ + 7.5 = +/- 5.937}[/tex]Step 5: Subtract the number that remains on the left side of the equation to find x, as follows:
[tex]x\text{ = +/- 5.937 - 7.5 }\Rightarrow x_{1=+5.937-7.5=-1.563,}x_{2\text{ = -5.937 - 7.5 = - 13.437}}[/tex]Now, we can asnwer the question, using the information from step 4 and 5:
56.25 would have been added to complete the square
