25x^2-88x-4=0

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Solution for 25x^2-88x-4=0 equation:


Simplifying
25x2 + -88x + -4 = 0

Reorder the terms:
-4 + -88x + 25x2 = 0

Solving
-4 + -88x + 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'.
-0.16 + -3.52x + x2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + -3.52x + 0.16 + x2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + -3.52x + x2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + -3.52x + x2 = 0 + 0.16
-3.52x + x2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
-3.52x + x2 = 0.16

The x term is -3.52x.  Take half its coefficient (-1.76).
Square it (3.0976) and add it to both sides.

Add '3.0976' to each side of the equation.
-3.52x + 3.0976 + x2 = 0.16 + 3.0976

Reorder the terms:
3.0976 + -3.52x + x2 = 0.16 + 3.0976

Combine like terms: 0.16 + 3.0976 = 3.2576
3.0976 + -3.52x + x2 = 3.2576

Factor a perfect square on the left side:
(x + -1.76)(x + -1.76) = 3.2576

Calculate the square root of the right side: 1.804882268

Break this problem into two subproblems by setting 
(x + -1.76) equal to 1.804882268 and -1.804882268.

Subproblem 1

x + -1.76 = 1.804882268 Simplifying x + -1.76 = 1.804882268 Reorder the terms: -1.76 + x = 1.804882268 Solving -1.76 + x = 1.804882268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.76' to each side of the equation. -1.76 + 1.76 + x = 1.804882268 + 1.76 Combine like terms: -1.76 + 1.76 = 0.00 0.00 + x = 1.804882268 + 1.76 x = 1.804882268 + 1.76 Combine like terms: 1.804882268 + 1.76 = 3.564882268 x = 3.564882268 Simplifying x = 3.564882268

Subproblem 2

x + -1.76 = -1.804882268 Simplifying x + -1.76 = -1.804882268 Reorder the terms: -1.76 + x = -1.804882268 Solving -1.76 + x = -1.804882268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.76' to each side of the equation. -1.76 + 1.76 + x = -1.804882268 + 1.76 Combine like terms: -1.76 + 1.76 = 0.00 0.00 + x = -1.804882268 + 1.76 x = -1.804882268 + 1.76 Combine like terms: -1.804882268 + 1.76 = -0.044882268 x = -0.044882268 Simplifying x = -0.044882268

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.564882268, -0.044882268}

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