MATH SOLVE

5 months ago

Q:
# How do I find the values for a, b, and c, to complete the solution?

Accepted Solution

A:

Answer:

The values a, b, and c are: a = - 4, b = 3, c = 6

The solutions to the equation are: x = - 4 + 3β6 and x = - 4 - 3β6

Explanation:

1) First step is complete squares:

xΒ² + 8x = 38 β given

xΒ² + 8x + (8/2)Β² = 38 + (8/4)Β² β add square of the half of 8

xΒ² + 8x + 16 = 38 + 16 β solve the parenthesis

xΒ² + 8xΒ + 16 = 54 β combine like terms

2) Second, solve the equation:

(x + 4)Β² = 54 β factor the perfect square trinomial

(x + 4) = +/- β54 β extract square root of both sides

x = - 4 +/- β54 β subtract 4 from both sides

x = -4 +/- 3β6 β simplify the root

x = - 4 + 3β6 and x = - 4 - 3β6 β separate the two solutions

3) Third, compare with the solutions shown:

x = a + bβc and x = a - bβc

β a = -4, b = 3, c = 6

The values a, b, and c are: a = - 4, b = 3, c = 6

The solutions to the equation are: x = - 4 + 3β6 and x = - 4 - 3β6

Explanation:

1) First step is complete squares:

xΒ² + 8x = 38 β given

xΒ² + 8x + (8/2)Β² = 38 + (8/4)Β² β add square of the half of 8

xΒ² + 8x + 16 = 38 + 16 β solve the parenthesis

xΒ² + 8xΒ + 16 = 54 β combine like terms

2) Second, solve the equation:

(x + 4)Β² = 54 β factor the perfect square trinomial

(x + 4) = +/- β54 β extract square root of both sides

x = - 4 +/- β54 β subtract 4 from both sides

x = -4 +/- 3β6 β simplify the root

x = - 4 + 3β6 and x = - 4 - 3β6 β separate the two solutions

3) Third, compare with the solutions shown:

x = a + bβc and x = a - bβc

β a = -4, b = 3, c = 6