Hmm, your answer looks like you were using the quadratic formula, rather than completing the square.But I’ll detail completing the square first, as that’s what you asked for.
First step: divide out “a”, the coefficient of the squared term. In this case 2.
2x^2 +18x = -28
x^2 + 9 x = -14
Second step: move the constant term to the right hand side.
It is already there, cool.
Third step: calculate b/2 from the current equation. Since b is now 9, b/2 is 9/2.
Fourth step: add (b/2)^2 to both sides. This “ completes the square“ because you can be certain that the left hand side is now the perfect square of (x+9/2).
(x+9/2)^2 = -14 + (9/2)^2
Simplify the right hand side.
(x+9/2)^2= -14 + 81/4
(x+9/2)^2 = (-56+81)/4
(x+9/2)^2 = 25/4
Fifth step: take the square roots of both sides (remember to keep both the positive and negative square roots of the right hand side.)
x+9/2 = ± 5/2
Sixth Step: write both solutions and solve them individually:
(pos): x+9/2 = +5/2
x = -4/2 = -2
(neg): x+ 9/2 = -5/2
x = -14/2 = -7
These answers both work.
If you had tried the quadratic formula, you should have started with
2x^2 +18x = -28
Put on left hand side
2x^2 +18x + 28 = 0
x = (-b ± sqrt(b^2 -4ac)) / 2a
Starting from original equation
x = (-18 ± sqrt(18*18 -4*2*28)) / 4
x = (-18)/4 ± sqrt(324-224)/4
x = -9/2 ± sqrt(100)/4
x = -9/2 ± 10/4
x = -9/2 ± 5/2
check these two techniques with your work to see where you went wrong. the two big causes of error are negative signs and dropping a digit.
Does this help? If not, ask again.
