2x^2+7x-140=0

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Solution for 2x^2+7x-140=0 equation:


Simplifying
2x2 + 7x + -140 = 0

Reorder the terms:
-140 + 7x + 2x2 = 0

Solving
-140 + 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'.
-70 + 3.5x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 3.5x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 3.5x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 3.5x + x2 = 0 + 70
3.5x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
3.5x + x2 = 70

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 = 70 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 70 + 3.0625

Combine like terms: 70 + 3.0625 = 73.0625
3.0625 + 3.5x + x2 = 73.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 73.0625

Calculate the square root of the right side: 8.547660499

Break this problem into two subproblems by setting 
(x + 1.75) equal to 8.547660499 and -8.547660499.

Subproblem 1

x + 1.75 = 8.547660499 Simplifying x + 1.75 = 8.547660499 Reorder the terms: 1.75 + x = 8.547660499 Solving 1.75 + x = 8.547660499 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 = 8.547660499 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 8.547660499 + -1.75 x = 8.547660499 + -1.75 Combine like terms: 8.547660499 + -1.75 = 6.797660499 x = 6.797660499 Simplifying x = 6.797660499

Subproblem 2

x + 1.75 = -8.547660499 Simplifying x + 1.75 = -8.547660499 Reorder the terms: 1.75 + x = -8.547660499 Solving 1.75 + x = -8.547660499 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 = -8.547660499 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -8.547660499 + -1.75 x = -8.547660499 + -1.75 Combine like terms: -8.547660499 + -1.75 = -10.297660499 x = -10.297660499 Simplifying x = -10.297660499

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.797660499, -10.297660499}

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