4x^2-3x-13=0

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


Simplifying
4x2 + -3x + -13 = 0

Reorder the terms:
-13 + -3x + 4x2 = 0

Solving
-13 + -3x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-3.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -0.75x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -0.75x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -0.75x + x2 = 0 + 3.25
-0.75x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-0.75x + x2 = 3.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 3.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 3.25 + 0.140625

Combine like terms: 3.25 + 0.140625 = 3.390625
0.140625 + -0.75x + x2 = 3.390625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 3.390625

Calculate the square root of the right side: 1.841364983

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.841364983 and -1.841364983.

Subproblem 1

x + -0.375 = 1.841364983 Simplifying x + -0.375 = 1.841364983 Reorder the terms: -0.375 + x = 1.841364983 Solving -0.375 + x = 1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.841364983 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.841364983 + 0.375 x = 1.841364983 + 0.375 Combine like terms: 1.841364983 + 0.375 = 2.216364983 x = 2.216364983 Simplifying x = 2.216364983

Subproblem 2

x + -0.375 = -1.841364983 Simplifying x + -0.375 = -1.841364983 Reorder the terms: -0.375 + x = -1.841364983 Solving -0.375 + x = -1.841364983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.841364983 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.841364983 + 0.375 x = -1.841364983 + 0.375 Combine like terms: -1.841364983 + 0.375 = -1.466364983 x = -1.466364983 Simplifying x = -1.466364983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.216364983, -1.466364983}

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