2.3x^2-25x-12.5=0

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Solution for 2.3x^2-25x-12.5=0 equation:


Simplifying
2.3x2 + -25x + -12.5 = 0

Reorder the terms:
-12.5 + -25x + 2.3x2 = 0

Solving
-12.5 + -25x + 2.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '2.3'.
-5.434782609 + -10.86956522x + x2 = 0

Move the constant term to the right:

Add '5.434782609' to each side of the equation.
-5.434782609 + -10.86956522x + 5.434782609 + x2 = 0 + 5.434782609

Reorder the terms:
-5.434782609 + 5.434782609 + -10.86956522x + x2 = 0 + 5.434782609

Combine like terms: -5.434782609 + 5.434782609 = 0.000000000
0.000000000 + -10.86956522x + x2 = 0 + 5.434782609
-10.86956522x + x2 = 0 + 5.434782609

Combine like terms: 0 + 5.434782609 = 5.434782609
-10.86956522x + x2 = 5.434782609

The x term is -10.86956522x.  Take half its coefficient (-5.43478261).
Square it (29.53686202) and add it to both sides.

Add '29.53686202' to each side of the equation.
-10.86956522x + 29.53686202 + x2 = 5.434782609 + 29.53686202

Reorder the terms:
29.53686202 + -10.86956522x + x2 = 5.434782609 + 29.53686202

Combine like terms: 5.434782609 + 29.53686202 = 34.971644629
29.53686202 + -10.86956522x + x2 = 34.971644629

Factor a perfect square on the left side:
(x + -5.43478261)(x + -5.43478261) = 34.971644629

Calculate the square root of the right side: 5.913682831

Break this problem into two subproblems by setting 
(x + -5.43478261) equal to 5.913682831 and -5.913682831.

Subproblem 1

x + -5.43478261 = 5.913682831 Simplifying x + -5.43478261 = 5.913682831 Reorder the terms: -5.43478261 + x = 5.913682831 Solving -5.43478261 + x = 5.913682831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.43478261' to each side of the equation. -5.43478261 + 5.43478261 + x = 5.913682831 + 5.43478261 Combine like terms: -5.43478261 + 5.43478261 = 0.00000000 0.00000000 + x = 5.913682831 + 5.43478261 x = 5.913682831 + 5.43478261 Combine like terms: 5.913682831 + 5.43478261 = 11.348465441 x = 11.348465441 Simplifying x = 11.348465441

Subproblem 2

x + -5.43478261 = -5.913682831 Simplifying x + -5.43478261 = -5.913682831 Reorder the terms: -5.43478261 + x = -5.913682831 Solving -5.43478261 + x = -5.913682831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.43478261' to each side of the equation. -5.43478261 + 5.43478261 + x = -5.913682831 + 5.43478261 Combine like terms: -5.43478261 + 5.43478261 = 0.00000000 0.00000000 + x = -5.913682831 + 5.43478261 x = -5.913682831 + 5.43478261 Combine like terms: -5.913682831 + 5.43478261 = -0.478900221 x = -0.478900221 Simplifying x = -0.478900221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.348465441, -0.478900221}

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