25x^2+50x-27=0

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Solution for 25x^2+50x-27=0 equation:


Simplifying
25x2 + 50x + -27 = 0

Reorder the terms:
-27 + 50x + 25x2 = 0

Solving
-27 + 50x + 25x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
-1.08 + 2x + x2 = 0

Move the constant term to the right:

Add '1.08' to each side of the equation.
-1.08 + 2x + 1.08 + x2 = 0 + 1.08

Reorder the terms:
-1.08 + 1.08 + 2x + x2 = 0 + 1.08

Combine like terms: -1.08 + 1.08 = 0.00
0.00 + 2x + x2 = 0 + 1.08
2x + x2 = 0 + 1.08

Combine like terms: 0 + 1.08 = 1.08
2x + x2 = 1.08

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.08 + 1

Reorder the terms:
1 + 2x + x2 = 1.08 + 1

Combine like terms: 1.08 + 1 = 2.08
1 + 2x + x2 = 2.08

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.08

Calculate the square root of the right side: 1.44222051

Break this problem into two subproblems by setting 
(x + 1) equal to 1.44222051 and -1.44222051.

Subproblem 1

x + 1 = 1.44222051 Simplifying x + 1 = 1.44222051 Reorder the terms: 1 + x = 1.44222051 Solving 1 + x = 1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.44222051 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.44222051 + -1 x = 1.44222051 + -1 Combine like terms: 1.44222051 + -1 = 0.44222051 x = 0.44222051 Simplifying x = 0.44222051

Subproblem 2

x + 1 = -1.44222051 Simplifying x + 1 = -1.44222051 Reorder the terms: 1 + x = -1.44222051 Solving 1 + x = -1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.44222051 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.44222051 + -1 x = -1.44222051 + -1 Combine like terms: -1.44222051 + -1 = -2.44222051 x = -2.44222051 Simplifying x = -2.44222051

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.44222051, -2.44222051}

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