Question

what is the solution set to the equation x^2+8x+16=49
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Answer 1

\[(x+4)^2=49\]

Answer 2

Take square root of both sides.

Answer 3

Oh, thank you :)

Answer 4

Simplifying
x2 + 8x + 16 = 49

Reorder the terms:
16 + 8x + x2 = 49

Solving
16 + 8x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
16 + -49 + 8x + x2 = 49 + -49

Combine like terms: 16 + -49 = -33
-33 + 8x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-33 + 8x + x2 = 0

Factor a trinomial.
(-11 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-11, 3}