Answer:
The values a, b, and c are: a = - 4, b = 3, c = 6
The solutions to the equation are: x = - 4 + 3√6 and x = - 4 - 3√6
Step-by-step explanation:
1) First step is complete squares:
x² + 8x = 38 ← given
x² + 8x + (8/2)² = 38 + (8/4)² ← add square of the half of 8
x² + 8x + 16 = 38 + 16 ← solve the parenthesis
x² + 8x + 16 = 54 ← combine like terms
2) Second, solve the equation:
(x + 4)² = 54 ← factor the perfect square trinomial
(x + 4) = +/- √54 ← extract square root of both sides
x = - 4 +/- √54 ← subtract 4 from both sides
x = -4 +/- 3√6 ← simplify the root
x = - 4 + 3√6 and x = - 4 - 3√6 ← separate the two solutions
3) Third, compare with the solutions shown:
x = a + b√c and x = a - b√c
⇒ a = -4, b = 3, c = 6