x^2+x-85=0

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


Simplifying
x2 + x + -85 = 0

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

Solving
-85 + x + 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 + x + 85 + x2 = 0 + 85

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 85 + 0.25

Reorder the terms:
0.25 + x + x2 = 85 + 0.25

Combine like terms: 85 + 0.25 = 85.25
0.25 + x + x2 = 85.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.233092656 and -9.233092656.

Subproblem 1

x + 0.5 = 9.233092656 Simplifying x + 0.5 = 9.233092656 Reorder the terms: 0.5 + x = 9.233092656 Solving 0.5 + x = 9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.233092656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.233092656 + -0.5 x = 9.233092656 + -0.5 Combine like terms: 9.233092656 + -0.5 = 8.733092656 x = 8.733092656 Simplifying x = 8.733092656

Subproblem 2

x + 0.5 = -9.233092656 Simplifying x + 0.5 = -9.233092656 Reorder the terms: 0.5 + x = -9.233092656 Solving 0.5 + x = -9.233092656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.233092656 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.233092656 + -0.5 x = -9.233092656 + -0.5 Combine like terms: -9.233092656 + -0.5 = -9.733092656 x = -9.733092656 Simplifying x = -9.733092656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.733092656, -9.733092656}

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