x^2+26x=750

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Solution for x^2+26x=750 equation:


Simplifying
x2 + 26x = 750

Reorder the terms:
26x + x2 = 750

Solving
26x + x2 = 750

Solving for variable 'x'.

Reorder the terms:
-750 + 26x + x2 = 750 + -750

Combine like terms: 750 + -750 = 0
-750 + 26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '750' to each side of the equation.
-750 + 26x + 750 + x2 = 0 + 750

Reorder the terms:
-750 + 750 + 26x + x2 = 0 + 750

Combine like terms: -750 + 750 = 0
0 + 26x + x2 = 0 + 750
26x + x2 = 0 + 750

Combine like terms: 0 + 750 = 750
26x + x2 = 750

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 = 750 + 169

Reorder the terms:
169 + 26x + x2 = 750 + 169

Combine like terms: 750 + 169 = 919
169 + 26x + x2 = 919

Factor a perfect square on the left side:
(x + 13)(x + 13) = 919

Calculate the square root of the right side: 30.315012782

Break this problem into two subproblems by setting 
(x + 13) equal to 30.315012782 and -30.315012782.

Subproblem 1

x + 13 = 30.315012782 Simplifying x + 13 = 30.315012782 Reorder the terms: 13 + x = 30.315012782 Solving 13 + x = 30.315012782 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 = 30.315012782 + -13 Combine like terms: 13 + -13 = 0 0 + x = 30.315012782 + -13 x = 30.315012782 + -13 Combine like terms: 30.315012782 + -13 = 17.315012782 x = 17.315012782 Simplifying x = 17.315012782

Subproblem 2

x + 13 = -30.315012782 Simplifying x + 13 = -30.315012782 Reorder the terms: 13 + x = -30.315012782 Solving 13 + x = -30.315012782 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 = -30.315012782 + -13 Combine like terms: 13 + -13 = 0 0 + x = -30.315012782 + -13 x = -30.315012782 + -13 Combine like terms: -30.315012782 + -13 = -43.315012782 x = -43.315012782 Simplifying x = -43.315012782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.315012782, -43.315012782}

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