Answer:
(x + 10)^2 + (-186)
Step-by-step explanation:
x^2 + 20x - 86 =
Move the constant term to the right leaving a space between the x-term and the constant term.
= x^2 + 20x - 86
To complete the square, take half of the x-term coefficient and square it.
Half of 20 is 10. 10 squared is 100. This is the number that completes the square. Add it right after the x-term. Now you need to subtract the same amount at the end.
= x^2 + 20x + 100 - 86 - 100
Since 100 was added and subtracted, the expression has the same value. The first three terms are a perfect square trinomial, so we write it as the square of a binomial.
= (x + 10)^2 - 186
Since you have an addition sign, we write -186 as a sum:
= (x + 10)^2 + (-186)
