2x^2+25x-9.5=0

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Solution for 2x^2+25x-9.5=0 equation:


Simplifying
2x2 + 25x + -9.5 = 0

Reorder the terms:
-9.5 + 25x + 2x2 = 0

Solving
-9.5 + 25x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-4.75 + 12.5x + x2 = 0

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 12.5x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 12.5x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 12.5x + x2 = 0 + 4.75
12.5x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
12.5x + x2 = 4.75

The x term is 12.5x.  Take half its coefficient (6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
12.5x + 39.0625 + x2 = 4.75 + 39.0625

Reorder the terms:
39.0625 + 12.5x + x2 = 4.75 + 39.0625

Combine like terms: 4.75 + 39.0625 = 43.8125
39.0625 + 12.5x + x2 = 43.8125

Factor a perfect square on the left side:
(x + 6.25)(x + 6.25) = 43.8125

Calculate the square root of the right side: 6.619101147

Break this problem into two subproblems by setting 
(x + 6.25) equal to 6.619101147 and -6.619101147.

Subproblem 1

x + 6.25 = 6.619101147 Simplifying x + 6.25 = 6.619101147 Reorder the terms: 6.25 + x = 6.619101147 Solving 6.25 + x = 6.619101147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = 6.619101147 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.619101147 + -6.25 x = 6.619101147 + -6.25 Combine like terms: 6.619101147 + -6.25 = 0.369101147 x = 0.369101147 Simplifying x = 0.369101147

Subproblem 2

x + 6.25 = -6.619101147 Simplifying x + 6.25 = -6.619101147 Reorder the terms: 6.25 + x = -6.619101147 Solving 6.25 + x = -6.619101147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.25' to each side of the equation. 6.25 + -6.25 + x = -6.619101147 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.619101147 + -6.25 x = -6.619101147 + -6.25 Combine like terms: -6.619101147 + -6.25 = -12.869101147 x = -12.869101147 Simplifying x = -12.869101147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.369101147, -12.869101147}

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