4x^2-8x-13=0

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Solution for 4x^2-8x-13=0 equation:


Simplifying
4x2 + -8x + -13 = 0

Reorder the terms:
-13 + -8x + 4x2 = 0

Solving
-13 + -8x + 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 + -2x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -2x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -2x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -2x + x2 = 0 + 3.25
-2x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-2x + x2 = 3.25

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 = 3.25 + 1

Reorder the terms:
1 + -2x + x2 = 3.25 + 1

Combine like terms: 3.25 + 1 = 4.25
1 + -2x + x2 = 4.25

Factor a perfect square on the left side:
(x + -1)(x + -1) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -1) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + -1 = 2.061552813 Simplifying x + -1 = 2.061552813 Reorder the terms: -1 + x = 2.061552813 Solving -1 + x = 2.061552813 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 = 2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.061552813 + 1 x = 2.061552813 + 1 Combine like terms: 2.061552813 + 1 = 3.061552813 x = 3.061552813 Simplifying x = 3.061552813

Subproblem 2

x + -1 = -2.061552813 Simplifying x + -1 = -2.061552813 Reorder the terms: -1 + x = -2.061552813 Solving -1 + x = -2.061552813 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 = -2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.061552813 + 1 x = -2.061552813 + 1 Combine like terms: -2.061552813 + 1 = -1.061552813 x = -1.061552813 Simplifying x = -1.061552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.061552813, -1.061552813}

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