2x^2+7x-7500=0

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Solution for 2x^2+7x-7500=0 equation:


Simplifying
2x2 + 7x + -7500 = 0

Reorder the terms:
-7500 + 7x + 2x2 = 0

Solving
-7500 + 7x + 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'.
-3750 + 3.5x + x2 = 0

Move the constant term to the right:

Add '3750' to each side of the equation.
-3750 + 3.5x + 3750 + x2 = 0 + 3750

Reorder the terms:
-3750 + 3750 + 3.5x + x2 = 0 + 3750

Combine like terms: -3750 + 3750 = 0
0 + 3.5x + x2 = 0 + 3750
3.5x + x2 = 0 + 3750

Combine like terms: 0 + 3750 = 3750
3.5x + x2 = 3750

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 3750 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 3750 + 3.0625

Combine like terms: 3750 + 3.0625 = 3753.0625
3.0625 + 3.5x + x2 = 3753.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 3753.0625

Calculate the square root of the right side: 61.262243674

Break this problem into two subproblems by setting 
(x + 1.75) equal to 61.262243674 and -61.262243674.

Subproblem 1

x + 1.75 = 61.262243674 Simplifying x + 1.75 = 61.262243674 Reorder the terms: 1.75 + x = 61.262243674 Solving 1.75 + x = 61.262243674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 61.262243674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 61.262243674 + -1.75 x = 61.262243674 + -1.75 Combine like terms: 61.262243674 + -1.75 = 59.512243674 x = 59.512243674 Simplifying x = 59.512243674

Subproblem 2

x + 1.75 = -61.262243674 Simplifying x + 1.75 = -61.262243674 Reorder the terms: 1.75 + x = -61.262243674 Solving 1.75 + x = -61.262243674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -61.262243674 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -61.262243674 + -1.75 x = -61.262243674 + -1.75 Combine like terms: -61.262243674 + -1.75 = -63.012243674 x = -63.012243674 Simplifying x = -63.012243674

Solution

The solution to the problem is based on the solutions from the subproblems. x = {59.512243674, -63.012243674}

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