2x^2+7x-20=0

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Solution for 2x^2+7x-20=0 equation:


Simplifying
2x2 + 7x + -20 = 0

Reorder the terms:
-20 + 7x + 2x2 = 0

Solving
-20 + 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'.
-10 + 3.5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 3.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 3.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3.5x + x2 = 0 + 10
3.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
3.5x + x2 = 10

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 = 10 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 10 + 3.0625

Combine like terms: 10 + 3.0625 = 13.0625
3.0625 + 3.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + 1.75) equal to 3.614208074 and -3.614208074.

Subproblem 1

x + 1.75 = 3.614208074 Simplifying x + 1.75 = 3.614208074 Reorder the terms: 1.75 + x = 3.614208074 Solving 1.75 + x = 3.614208074 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 = 3.614208074 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.614208074 + -1.75 x = 3.614208074 + -1.75 Combine like terms: 3.614208074 + -1.75 = 1.864208074 x = 1.864208074 Simplifying x = 1.864208074

Subproblem 2

x + 1.75 = -3.614208074 Simplifying x + 1.75 = -3.614208074 Reorder the terms: 1.75 + x = -3.614208074 Solving 1.75 + x = -3.614208074 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 = -3.614208074 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.614208074 + -1.75 x = -3.614208074 + -1.75 Combine like terms: -3.614208074 + -1.75 = -5.364208074 x = -5.364208074 Simplifying x = -5.364208074

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.864208074, -5.364208074}

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