3+4x-13x^2=0

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Solution for 3+4x-13x^2=0 equation:


Simplifying
3 + 4x + -13x2 = 0

Solving
3 + 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'.
-0.2307692308 + -0.3076923077x + x2 = 0

Move the constant term to the right:

Add '0.2307692308' to each side of the equation.
-0.2307692308 + -0.3076923077x + 0.2307692308 + x2 = 0 + 0.2307692308

Reorder the terms:
-0.2307692308 + 0.2307692308 + -0.3076923077x + x2 = 0 + 0.2307692308

Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000
0.0000000000 + -0.3076923077x + x2 = 0 + 0.2307692308
-0.3076923077x + x2 = 0 + 0.2307692308

Combine like terms: 0 + 0.2307692308 = 0.2307692308
-0.3076923077x + x2 = 0.2307692308

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 = 0.2307692308 + 0.02366863907

Reorder the terms:
0.02366863907 + -0.3076923077x + x2 = 0.2307692308 + 0.02366863907

Combine like terms: 0.2307692308 + 0.02366863907 = 0.25443786987
0.02366863907 + -0.3076923077x + x2 = 0.25443786987

Factor a perfect square on the left side:
(x + -0.1538461539)(x + -0.1538461539) = 0.25443786987

Calculate the square root of the right side: 0.504418348

Break this problem into two subproblems by setting 
(x + -0.1538461539) equal to 0.504418348 and -0.504418348.

Subproblem 1

x + -0.1538461539 = 0.504418348 Simplifying x + -0.1538461539 = 0.504418348 Reorder the terms: -0.1538461539 + x = 0.504418348 Solving -0.1538461539 + x = 0.504418348 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 = 0.504418348 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = 0.504418348 + 0.1538461539 x = 0.504418348 + 0.1538461539 Combine like terms: 0.504418348 + 0.1538461539 = 0.6582645019 x = 0.6582645019 Simplifying x = 0.6582645019

Subproblem 2

x + -0.1538461539 = -0.504418348 Simplifying x + -0.1538461539 = -0.504418348 Reorder the terms: -0.1538461539 + x = -0.504418348 Solving -0.1538461539 + x = -0.504418348 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 = -0.504418348 + 0.1538461539 Combine like terms: -0.1538461539 + 0.1538461539 = 0.0000000000 0.0000000000 + x = -0.504418348 + 0.1538461539 x = -0.504418348 + 0.1538461539 Combine like terms: -0.504418348 + 0.1538461539 = -0.3505721941 x = -0.3505721941 Simplifying x = -0.3505721941

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6582645019, -0.3505721941}

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