x^2+6x-66=-10

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Solution for x^2+6x-66=-10 equation:


Simplifying
x2 + 6x + -66 = -10

Reorder the terms:
-66 + 6x + x2 = -10

Solving
-66 + 6x + x2 = -10

Solving for variable 'x'.

Reorder the terms:
-66 + 10 + 6x + x2 = -10 + 10

Combine like terms: -66 + 10 = -56
-56 + 6x + x2 = -10 + 10

Combine like terms: -10 + 10 = 0
-56 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 6x + 56 + x2 = 0 + 56

Reorder the terms:
-56 + 56 + 6x + x2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 6x + x2 = 0 + 56
6x + x2 = 0 + 56

Combine like terms: 0 + 56 = 56
6x + x2 = 56

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 56 + 9

Reorder the terms:
9 + 6x + x2 = 56 + 9

Combine like terms: 56 + 9 = 65
9 + 6x + x2 = 65

Factor a perfect square on the left side:
(x + 3)(x + 3) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(x + 3) equal to 8.062257748 and -8.062257748.

Subproblem 1

x + 3 = 8.062257748 Simplifying x + 3 = 8.062257748 Reorder the terms: 3 + x = 8.062257748 Solving 3 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = 8.062257748 + -3 x = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 x = 5.062257748 Simplifying x = 5.062257748

Subproblem 2

x + 3 = -8.062257748 Simplifying x + 3 = -8.062257748 Reorder the terms: 3 + x = -8.062257748 Solving 3 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + x = -8.062257748 + -3 x = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 x = -11.062257748 Simplifying x = -11.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.062257748, -11.062257748}

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