0=13x^2+26x-249.73

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Solution for 0=13x^2+26x-249.73 equation:


Simplifying
0 = 13x2 + 26x + -249.73

Reorder the terms:
0 = -249.73 + 26x + 13x2

Solving
0 = -249.73 + 26x + 13x2

Solving for variable 'x'.

Combine like terms: 0 + 249.73 = 249.73
249.73 + -26x + -13x2 = -249.73 + 26x + 13x2 + 249.73 + -26x + -13x2

Reorder the terms:
249.73 + -26x + -13x2 = -249.73 + 249.73 + 26x + -26x + 13x2 + -13x2

Combine like terms: -249.73 + 249.73 = 0.00
249.73 + -26x + -13x2 = 0.00 + 26x + -26x + 13x2 + -13x2
249.73 + -26x + -13x2 = 26x + -26x + 13x2 + -13x2

Combine like terms: 26x + -26x = 0
249.73 + -26x + -13x2 = 0 + 13x2 + -13x2
249.73 + -26x + -13x2 = 13x2 + -13x2

Combine like terms: 13x2 + -13x2 = 0
249.73 + -26x + -13x2 = 0

Begin completing the square.  Divide all terms by
-13 the coefficient of the squared term: 

Divide each side by '-13'.
-19.21 + 2x + x2 = 0

Move the constant term to the right:

Add '19.21' to each side of the equation.
-19.21 + 2x + 19.21 + x2 = 0 + 19.21

Reorder the terms:
-19.21 + 19.21 + 2x + x2 = 0 + 19.21

Combine like terms: -19.21 + 19.21 = 0.00
0.00 + 2x + x2 = 0 + 19.21
2x + x2 = 0 + 19.21

Combine like terms: 0 + 19.21 = 19.21
2x + x2 = 19.21

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 19.21 + 1

Reorder the terms:
1 + 2x + x2 = 19.21 + 1

Combine like terms: 19.21 + 1 = 20.21
1 + 2x + x2 = 20.21

Factor a perfect square on the left side:
(x + 1)(x + 1) = 20.21

Calculate the square root of the right side: 4.495553359

Break this problem into two subproblems by setting 
(x + 1) equal to 4.495553359 and -4.495553359.

Subproblem 1

x + 1 = 4.495553359 Simplifying x + 1 = 4.495553359 Reorder the terms: 1 + x = 4.495553359 Solving 1 + x = 4.495553359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.495553359 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.495553359 + -1 x = 4.495553359 + -1 Combine like terms: 4.495553359 + -1 = 3.495553359 x = 3.495553359 Simplifying x = 3.495553359

Subproblem 2

x + 1 = -4.495553359 Simplifying x + 1 = -4.495553359 Reorder the terms: 1 + x = -4.495553359 Solving 1 + x = -4.495553359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.495553359 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.495553359 + -1 x = -4.495553359 + -1 Combine like terms: -4.495553359 + -1 = -5.495553359 x = -5.495553359 Simplifying x = -5.495553359

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.495553359, -5.495553359}

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