2x^2-25x-33=0

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Solution for 2x^2-25x-33=0 equation:


Simplifying
2x2 + -25x + -33 = 0

Reorder the terms:
-33 + -25x + 2x2 = 0

Solving
-33 + -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'.
-16.5 + -12.5x + x2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + -12.5x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + -12.5x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + -12.5x + x2 = 0 + 16.5
-12.5x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
-12.5x + x2 = 16.5

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 = 16.5 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 16.5 + 39.0625

Combine like terms: 16.5 + 39.0625 = 55.5625
39.0625 + -12.5x + x2 = 55.5625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 55.5625

Calculate the square root of the right side: 7.454025758

Break this problem into two subproblems by setting 
(x + -6.25) equal to 7.454025758 and -7.454025758.

Subproblem 1

x + -6.25 = 7.454025758 Simplifying x + -6.25 = 7.454025758 Reorder the terms: -6.25 + x = 7.454025758 Solving -6.25 + x = 7.454025758 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 = 7.454025758 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.454025758 + 6.25 x = 7.454025758 + 6.25 Combine like terms: 7.454025758 + 6.25 = 13.704025758 x = 13.704025758 Simplifying x = 13.704025758

Subproblem 2

x + -6.25 = -7.454025758 Simplifying x + -6.25 = -7.454025758 Reorder the terms: -6.25 + x = -7.454025758 Solving -6.25 + x = -7.454025758 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 = -7.454025758 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.454025758 + 6.25 x = -7.454025758 + 6.25 Combine like terms: -7.454025758 + 6.25 = -1.204025758 x = -1.204025758 Simplifying x = -1.204025758

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.704025758, -1.204025758}

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