20x^2-x-80=0

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Solution for 20x^2-x-80=0 equation:


Simplifying
20x2 + -1x + -80 = 0

Reorder the terms:
-80 + -1x + 20x2 = 0

Solving
-80 + -1x + 20x2 = 0

Solving for variable 'x'.

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

Divide each side by '20'.
-4 + -0.05x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -0.05x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -0.05x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -0.05x + x2 = 0 + 4
-0.05x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-0.05x + x2 = 4

The x term is -0.05x.  Take half its coefficient (-0.025).
Square it (0.000625) and add it to both sides.

Add '0.000625' to each side of the equation.
-0.05x + 0.000625 + x2 = 4 + 0.000625

Reorder the terms:
0.000625 + -0.05x + x2 = 4 + 0.000625

Combine like terms: 4 + 0.000625 = 4.000625
0.000625 + -0.05x + x2 = 4.000625

Factor a perfect square on the left side:
(x + -0.025)(x + -0.025) = 4.000625

Calculate the square root of the right side: 2.000156244

Break this problem into two subproblems by setting 
(x + -0.025) equal to 2.000156244 and -2.000156244.

Subproblem 1

x + -0.025 = 2.000156244 Simplifying x + -0.025 = 2.000156244 Reorder the terms: -0.025 + x = 2.000156244 Solving -0.025 + x = 2.000156244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 2.000156244 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 2.000156244 + 0.025 x = 2.000156244 + 0.025 Combine like terms: 2.000156244 + 0.025 = 2.025156244 x = 2.025156244 Simplifying x = 2.025156244

Subproblem 2

x + -0.025 = -2.000156244 Simplifying x + -0.025 = -2.000156244 Reorder the terms: -0.025 + x = -2.000156244 Solving -0.025 + x = -2.000156244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -2.000156244 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -2.000156244 + 0.025 x = -2.000156244 + 0.025 Combine like terms: -2.000156244 + 0.025 = -1.975156244 x = -1.975156244 Simplifying x = -1.975156244

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.025156244, -1.975156244}

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