x^2+14x+52=3

Solution for x^2+14x+52=3 equation:

Simplifying
x2 + 14x + 52 = 3

Reorder the terms:
52 + 14x + x2 = 3

Solving
52 + 14x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
52 + -3 + 14x + x2 = 3 + -3

Combine like terms: 52 + -3 = 49
49 + 14x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
49 + 14x + x2 = 0

Factor a trinomial.
(7 + x)(7 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {-7, -7}