x^2+11x=32

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Solution for x^2+11x=32 equation:


Simplifying
x2 + 11x = 32

Reorder the terms:
11x + x2 = 32

Solving
11x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + 11x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 11x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 11x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 11x + x2 = 0 + 32
11x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
11x + x2 = 32

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 = 32 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 32 + 30.25

Combine like terms: 32 + 30.25 = 62.25
30.25 + 11x + x2 = 62.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + 5.5 = 7.889866919 Simplifying x + 5.5 = 7.889866919 Reorder the terms: 5.5 + x = 7.889866919 Solving 5.5 + x = 7.889866919 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 = 7.889866919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 7.889866919 + -5.5 x = 7.889866919 + -5.5 Combine like terms: 7.889866919 + -5.5 = 2.389866919 x = 2.389866919 Simplifying x = 2.389866919

Subproblem 2

x + 5.5 = -7.889866919 Simplifying x + 5.5 = -7.889866919 Reorder the terms: 5.5 + x = -7.889866919 Solving 5.5 + x = -7.889866919 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 = -7.889866919 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -7.889866919 + -5.5 x = -7.889866919 + -5.5 Combine like terms: -7.889866919 + -5.5 = -13.389866919 x = -13.389866919 Simplifying x = -13.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.389866919, -13.389866919}

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