x^2+26x-334=0

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Solution for x^2+26x-334=0 equation:


Simplifying
x2 + 26x + -334 = 0

Reorder the terms:
-334 + 26x + x2 = 0

Solving
-334 + 26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '334' to each side of the equation.
-334 + 26x + 334 + x2 = 0 + 334

Reorder the terms:
-334 + 334 + 26x + x2 = 0 + 334

Combine like terms: -334 + 334 = 0
0 + 26x + x2 = 0 + 334
26x + x2 = 0 + 334

Combine like terms: 0 + 334 = 334
26x + x2 = 334

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = 334 + 169

Reorder the terms:
169 + 26x + x2 = 334 + 169

Combine like terms: 334 + 169 = 503
169 + 26x + x2 = 503

Factor a perfect square on the left side:
(x + 13)(x + 13) = 503

Calculate the square root of the right side: 22.427661492

Break this problem into two subproblems by setting 
(x + 13) equal to 22.427661492 and -22.427661492.

Subproblem 1

x + 13 = 22.427661492 Simplifying x + 13 = 22.427661492 Reorder the terms: 13 + x = 22.427661492 Solving 13 + x = 22.427661492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 22.427661492 + -13 Combine like terms: 13 + -13 = 0 0 + x = 22.427661492 + -13 x = 22.427661492 + -13 Combine like terms: 22.427661492 + -13 = 9.427661492 x = 9.427661492 Simplifying x = 9.427661492

Subproblem 2

x + 13 = -22.427661492 Simplifying x + 13 = -22.427661492 Reorder the terms: 13 + x = -22.427661492 Solving 13 + x = -22.427661492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -22.427661492 + -13 Combine like terms: 13 + -13 = 0 0 + x = -22.427661492 + -13 x = -22.427661492 + -13 Combine like terms: -22.427661492 + -13 = -35.427661492 x = -35.427661492 Simplifying x = -35.427661492

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.427661492, -35.427661492}

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