-13x^2+4x+260=0

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Solution for -13x^2+4x+260=0 equation:


Simplifying
-13x2 + 4x + 260 = 0

Reorder the terms:
260 + 4x + -13x2 = 0

Solving
260 + 4x + -13x2 = 0

Solving for variable 'x'.

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

Divide each side by '-13'.
-20 + -0.3076923077x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -0.3076923077x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -0.3076923077x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -0.3076923077x + x2 = 0 + 20
-0.3076923077x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-0.3076923077x + x2 = 20

The x term is -0.3076923077x.  Take half its coefficient (-0.1538461539).
Square it (0.02366863907) and add it to both sides.

Add '0.02366863907' to each side of the equation.
-0.3076923077x + 0.02366863907 + x2 = 20 + 0.02366863907

Reorder the terms:
0.02366863907 + -0.3076923077x + x2 = 20 + 0.02366863907

Combine like terms: 20 + 0.02366863907 = 20.02366863907
0.02366863907 + -0.3076923077x + x2 = 20.02366863907

Factor a perfect square on the left side:
(x + -0.1538461539)(x + -0.1538461539) = 20.02366863907

Calculate the square root of the right side: 4.474781407

Break this problem into two subproblems by setting 
(x + -0.1538461539) equal to 4.474781407 and -4.474781407.

Subproblem 1

x + -0.1538461539 = 4.474781407 Simplifying x + -0.1538461539 = 4.474781407 Reorder the terms: -0.1538461539 + x = 4.474781407 Solving -0.1538461539 + x = 4.474781407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = 4.474781407 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 4.474781407 + 0.1538461539 x = 4.474781407 + 0.1538461539 Combine like terms: 4.474781407 + 0.1538461539 = 4.6286275609 x = 4.6286275609 Simplifying x = 4.6286275609

Subproblem 2

x + -0.1538461539 = -4.474781407 Simplifying x + -0.1538461539 = -4.474781407 Reorder the terms: -0.1538461539 + x = -4.474781407 Solving -0.1538461539 + x = -4.474781407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1538461539' to each side of the equation. -0.1538461539 + 0.1538461539 + x = -4.474781407 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -4.474781407 + 0.1538461539 x = -4.474781407 + 0.1538461539 Combine like terms: -4.474781407 + 0.1538461539 = -4.3209352531 x = -4.3209352531 Simplifying x = -4.3209352531

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.6286275609, -4.3209352531}

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