2x^2-3x-40=0

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Solution for 2x^2-3x-40=0 equation:


Simplifying
2x2 + -3x + -40 = 0

Reorder the terms:
-40 + -3x + 2x2 = 0

Solving
-40 + -3x + 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'.
-20 + -1.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -1.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -1.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1.5x + x2 = 0 + 20
-1.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-1.5x + x2 = 20

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 20 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 20 + 0.5625

Combine like terms: 20 + 0.5625 = 20.5625
0.5625 + -1.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + -0.75) equal to 4.534589287 and -4.534589287.

Subproblem 1

x + -0.75 = 4.534589287 Simplifying x + -0.75 = 4.534589287 Reorder the terms: -0.75 + x = 4.534589287 Solving -0.75 + x = 4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 4.534589287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 4.534589287 + 0.75 x = 4.534589287 + 0.75 Combine like terms: 4.534589287 + 0.75 = 5.284589287 x = 5.284589287 Simplifying x = 5.284589287

Subproblem 2

x + -0.75 = -4.534589287 Simplifying x + -0.75 = -4.534589287 Reorder the terms: -0.75 + x = -4.534589287 Solving -0.75 + x = -4.534589287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -4.534589287 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -4.534589287 + 0.75 x = -4.534589287 + 0.75 Combine like terms: -4.534589287 + 0.75 = -3.784589287 x = -3.784589287 Simplifying x = -3.784589287

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.284589287, -3.784589287}

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