2x^2-16x-26=0

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Solution for 2x^2-16x-26=0 equation:


Simplifying
2x2 + -16x + -26 = 0

Reorder the terms:
-26 + -16x + 2x2 = 0

Solving
-26 + -16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-13 + -8x + x2)' equal to zero and attempt to solve: Simplifying -13 + -8x + x2 = 0 Solving -13 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -8x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -8x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -8x + x2 = 0 + 13 -8x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -8x + x2 = 13 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 13 + 16 Reorder the terms: 16 + -8x + x2 = 13 + 16 Combine like terms: 13 + 16 = 29 16 + -8x + x2 = 29 Factor a perfect square on the left side: (x + -4)(x + -4) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -4) equal to 5.385164807 and -5.385164807.

Subproblem 1

x + -4 = 5.385164807 Simplifying x + -4 = 5.385164807 Reorder the terms: -4 + x = 5.385164807 Solving -4 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.385164807 + 4 x = 5.385164807 + 4 Combine like terms: 5.385164807 + 4 = 9.385164807 x = 9.385164807 Simplifying x = 9.385164807

Subproblem 2

x + -4 = -5.385164807 Simplifying x + -4 = -5.385164807 Reorder the terms: -4 + x = -5.385164807 Solving -4 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.385164807 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.385164807 + 4 x = -5.385164807 + 4 Combine like terms: -5.385164807 + 4 = -1.385164807 x = -1.385164807 Simplifying x = -1.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.385164807, -1.385164807}

Solution

x = {9.385164807, -1.385164807}

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