1x^2+25x=15

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Solution for 1x^2+25x=15 equation:


Simplifying
1x2 + 25x = 15

Reorder the terms:
25x + 1x2 = 15

Solving
25x + 1x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 25x + 1x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 25x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 25x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 25x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 25x + x2 = 0 + 15
25x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
25x + x2 = 15

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 15 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 15 + 156.25

Combine like terms: 15 + 156.25 = 171.25
156.25 + 25x + x2 = 171.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 171.25

Calculate the square root of the right side: 13.086252328

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.086252328 and -13.086252328.

Subproblem 1

x + 12.5 = 13.086252328 Simplifying x + 12.5 = 13.086252328 Reorder the terms: 12.5 + x = 13.086252328 Solving 12.5 + x = 13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 13.086252328 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.086252328 + -12.5 x = 13.086252328 + -12.5 Combine like terms: 13.086252328 + -12.5 = 0.586252328 x = 0.586252328 Simplifying x = 0.586252328

Subproblem 2

x + 12.5 = -13.086252328 Simplifying x + 12.5 = -13.086252328 Reorder the terms: 12.5 + x = -13.086252328 Solving 12.5 + x = -13.086252328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -13.086252328 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.086252328 + -12.5 x = -13.086252328 + -12.5 Combine like terms: -13.086252328 + -12.5 = -25.586252328 x = -25.586252328 Simplifying x = -25.586252328

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.586252328, -25.586252328}

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