Solve 2x^2+8x-7=-2 by completing the square

How to complete the square:

Step 1: Get all constants on one side.



Step 2: If x² has a coefficient, divide it out.



Step 3: Halve the coefficient of x, square it, and add it to both sides.
(In this case, half of 4 is 2, and 2² is 4, so we add 4 to both sides.



Step 4: Factor the left side. (And if the right side is a mixed number, change it to an improper fraction to make step 5 easier)
We set it up so that it will be a perfect square trinomial, so it'll always be equal to (x+half the coefficient of x)².



Step 5: Take the square root of each side.

(x+2)^2=\frac{13}2\\\sqrt{(x+2)^2}=\sqrt{\frac{13}2}

Step 6: Simplify and solve for x.



(Decimal answers if needed: approx -4.5495 and 0.54951)