x^2+11x-86=0

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Solution for x^2+11x-86=0 equation:


Simplifying
x2 + 11x + -86 = 0

Reorder the terms:
-86 + 11x + x2 = 0

Solving
-86 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '86' to each side of the equation.
-86 + 11x + 86 + x2 = 0 + 86

Reorder the terms:
-86 + 86 + 11x + x2 = 0 + 86

Combine like terms: -86 + 86 = 0
0 + 11x + x2 = 0 + 86
11x + x2 = 0 + 86

Combine like terms: 0 + 86 = 86
11x + x2 = 86

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 86 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 86 + 30.25

Combine like terms: 86 + 30.25 = 116.25
30.25 + 11x + x2 = 116.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 116.25

Calculate the square root of the right side: 10.781929326

Break this problem into two subproblems by setting 
(x + 5.5) equal to 10.781929326 and -10.781929326.

Subproblem 1

x + 5.5 = 10.781929326 Simplifying x + 5.5 = 10.781929326 Reorder the terms: 5.5 + x = 10.781929326 Solving 5.5 + x = 10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 10.781929326 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 10.781929326 + -5.5 x = 10.781929326 + -5.5 Combine like terms: 10.781929326 + -5.5 = 5.281929326 x = 5.281929326 Simplifying x = 5.281929326

Subproblem 2

x + 5.5 = -10.781929326 Simplifying x + 5.5 = -10.781929326 Reorder the terms: 5.5 + x = -10.781929326 Solving 5.5 + x = -10.781929326 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -10.781929326 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -10.781929326 + -5.5 x = -10.781929326 + -5.5 Combine like terms: -10.781929326 + -5.5 = -16.281929326 x = -16.281929326 Simplifying x = -16.281929326

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.281929326, -16.281929326}

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