Answer:
(a) x = -5 ± √21
Step-by-step explanation:
You want the solution to 2x² +20x +8 = 0 using the "completing the square" method.
It can be less confusing to divide the equation by the leading coefficient and separate the variable terms from the constant term:
2x² +20x +8 = 0
x² +10x +4 = 0 . . . . . . . divide by 2
x² +10x = -4 . . . . . . . . subtract 4
To complete the square, we add the square of half the x-coefficient:
x² +10x +25 = -4 +25 . . . . . . . (10/2)² = 5² = 25
(x +5)² = 21
To find the solution, we take the square root of both sides:
x +5 = ±√21
x = -5 ±√21 . . . . . . subtract 5
The solution is x = -5+√21 and x = -5-√21, matching the first choice.
