26x+x^2=112

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Solution for 26x+x^2=112 equation:


Simplifying
26x + x2 = 112

Solving
26x + x2 = 112

Solving for variable 'x'.

Reorder the terms:
-112 + 26x + x2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + 26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + 26x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + 26x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + 26x + x2 = 0 + 112
26x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
26x + x2 = 112

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 = 112 + 169

Reorder the terms:
169 + 26x + x2 = 112 + 169

Combine like terms: 112 + 169 = 281
169 + 26x + x2 = 281

Factor a perfect square on the left side:
(x + 13)(x + 13) = 281

Calculate the square root of the right side: 16.763054614

Break this problem into two subproblems by setting 
(x + 13) equal to 16.763054614 and -16.763054614.

Subproblem 1

x + 13 = 16.763054614 Simplifying x + 13 = 16.763054614 Reorder the terms: 13 + x = 16.763054614 Solving 13 + x = 16.763054614 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 = 16.763054614 + -13 Combine like terms: 13 + -13 = 0 0 + x = 16.763054614 + -13 x = 16.763054614 + -13 Combine like terms: 16.763054614 + -13 = 3.763054614 x = 3.763054614 Simplifying x = 3.763054614

Subproblem 2

x + 13 = -16.763054614 Simplifying x + 13 = -16.763054614 Reorder the terms: 13 + x = -16.763054614 Solving 13 + x = -16.763054614 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 = -16.763054614 + -13 Combine like terms: 13 + -13 = 0 0 + x = -16.763054614 + -13 x = -16.763054614 + -13 Combine like terms: -16.763054614 + -13 = -29.763054614 x = -29.763054614 Simplifying x = -29.763054614

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.763054614, -29.763054614}

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