0=2x^2-7x-40

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Solution for 0=2x^2-7x-40 equation:


Simplifying
0 = 2x2 + -7x + -40

Reorder the terms:
0 = -40 + -7x + 2x2

Solving
0 = -40 + -7x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 40 = 40
40 + 7x + -2x2 = -40 + -7x + 2x2 + 40 + 7x + -2x2

Reorder the terms:
40 + 7x + -2x2 = -40 + 40 + -7x + 7x + 2x2 + -2x2

Combine like terms: -40 + 40 = 0
40 + 7x + -2x2 = 0 + -7x + 7x + 2x2 + -2x2
40 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2

Combine like terms: -7x + 7x = 0
40 + 7x + -2x2 = 0 + 2x2 + -2x2
40 + 7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + 7x + -2x2 = 0

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

Divide each side by '-2'.
-20 + -3.5x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -3.5x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -3.5x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -3.5x + x2 = 0 + 20
-3.5x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-3.5x + x2 = 20

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 = 20 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 20 + 3.0625

Combine like terms: 20 + 3.0625 = 23.0625
3.0625 + -3.5x + x2 = 23.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(x + -1.75) equal to 4.802343178 and -4.802343178.

Subproblem 1

x + -1.75 = 4.802343178 Simplifying x + -1.75 = 4.802343178 Reorder the terms: -1.75 + x = 4.802343178 Solving -1.75 + x = 4.802343178 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 = 4.802343178 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 4.802343178 + 1.75 x = 4.802343178 + 1.75 Combine like terms: 4.802343178 + 1.75 = 6.552343178 x = 6.552343178 Simplifying x = 6.552343178

Subproblem 2

x + -1.75 = -4.802343178 Simplifying x + -1.75 = -4.802343178 Reorder the terms: -1.75 + x = -4.802343178 Solving -1.75 + x = -4.802343178 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 = -4.802343178 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -4.802343178 + 1.75 x = -4.802343178 + 1.75 Combine like terms: -4.802343178 + 1.75 = -3.052343178 x = -3.052343178 Simplifying x = -3.052343178

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.552343178, -3.052343178}

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