x^2+11x=13

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Solution for x^2+11x=13 equation:


Simplifying
x2 + 11x = 13

Reorder the terms:
11x + x2 = 13

Solving
11x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 11x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 11x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 11x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 11x + x2 = 0 + 13
11x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
11x + x2 = 13

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 = 13 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 13 + 30.25

Combine like terms: 13 + 30.25 = 43.25
30.25 + 11x + x2 = 43.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 43.25

Calculate the square root of the right side: 6.576473219

Break this problem into two subproblems by setting 
(x + 5.5) equal to 6.576473219 and -6.576473219.

Subproblem 1

x + 5.5 = 6.576473219 Simplifying x + 5.5 = 6.576473219 Reorder the terms: 5.5 + x = 6.576473219 Solving 5.5 + x = 6.576473219 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 = 6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.576473219 + -5.5 x = 6.576473219 + -5.5 Combine like terms: 6.576473219 + -5.5 = 1.076473219 x = 1.076473219 Simplifying x = 1.076473219

Subproblem 2

x + 5.5 = -6.576473219 Simplifying x + 5.5 = -6.576473219 Reorder the terms: 5.5 + x = -6.576473219 Solving 5.5 + x = -6.576473219 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 = -6.576473219 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.576473219 + -5.5 x = -6.576473219 + -5.5 Combine like terms: -6.576473219 + -5.5 = -12.076473219 x = -12.076473219 Simplifying x = -12.076473219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.076473219, -12.076473219}

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