x^2-26x+142=0

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Solution for x^2-26x+142=0 equation:


Simplifying
x2 + -26x + 142 = 0

Reorder the terms:
142 + -26x + x2 = 0

Solving
142 + -26x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-142' to each side of the equation.
142 + -26x + -142 + x2 = 0 + -142

Reorder the terms:
142 + -142 + -26x + x2 = 0 + -142

Combine like terms: 142 + -142 = 0
0 + -26x + x2 = 0 + -142
-26x + x2 = 0 + -142

Combine like terms: 0 + -142 = -142
-26x + x2 = -142

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 = -142 + 169

Reorder the terms:
169 + -26x + x2 = -142 + 169

Combine like terms: -142 + 169 = 27
169 + -26x + x2 = 27

Factor a perfect square on the left side:
(x + -13)(x + -13) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(x + -13) equal to 5.196152423 and -5.196152423.

Subproblem 1

x + -13 = 5.196152423 Simplifying x + -13 = 5.196152423 Reorder the terms: -13 + x = 5.196152423 Solving -13 + x = 5.196152423 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 = 5.196152423 + 13 Combine like terms: -13 + 13 = 0 0 + x = 5.196152423 + 13 x = 5.196152423 + 13 Combine like terms: 5.196152423 + 13 = 18.196152423 x = 18.196152423 Simplifying x = 18.196152423

Subproblem 2

x + -13 = -5.196152423 Simplifying x + -13 = -5.196152423 Reorder the terms: -13 + x = -5.196152423 Solving -13 + x = -5.196152423 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 = -5.196152423 + 13 Combine like terms: -13 + 13 = 0 0 + x = -5.196152423 + 13 x = -5.196152423 + 13 Combine like terms: -5.196152423 + 13 = 7.803847577 x = 7.803847577 Simplifying x = 7.803847577

Solution

The solution to the problem is based on the solutions from the subproblems. x = {18.196152423, 7.803847577}

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