x^2+6x-85=0

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Solution for x^2+6x-85=0 equation:


Simplifying
x2 + 6x + -85 = 0

Reorder the terms:
-85 + 6x + x2 = 0

Solving
-85 + 6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 6x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + 6x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + 6x + x2 = 0 + 85
6x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
6x + x2 = 85

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 = 85 + 9

Reorder the terms:
9 + 6x + x2 = 85 + 9

Combine like terms: 85 + 9 = 94
9 + 6x + x2 = 94

Factor a perfect square on the left side:
(x + 3)(x + 3) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(x + 3) equal to 9.695359715 and -9.695359715.

Subproblem 1

x + 3 = 9.695359715 Simplifying x + 3 = 9.695359715 Reorder the terms: 3 + x = 9.695359715 Solving 3 + x = 9.695359715 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 = 9.695359715 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.695359715 + -3 x = 9.695359715 + -3 Combine like terms: 9.695359715 + -3 = 6.695359715 x = 6.695359715 Simplifying x = 6.695359715

Subproblem 2

x + 3 = -9.695359715 Simplifying x + 3 = -9.695359715 Reorder the terms: 3 + x = -9.695359715 Solving 3 + x = -9.695359715 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 = -9.695359715 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.695359715 + -3 x = -9.695359715 + -3 Combine like terms: -9.695359715 + -3 = -12.695359715 x = -12.695359715 Simplifying x = -12.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.695359715, -12.695359715}

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