20x^2-10x-20=0

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Solution for 20x^2-10x-20=0 equation:


Simplifying
20x2 + -10x + -20 = 0

Reorder the terms:
-20 + -10x + 20x2 = 0

Solving
-20 + -10x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-2 + -1x + 2x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-2 + -1x + 2x2)' equal to zero and attempt to solve: Simplifying -2 + -1x + 2x2 = 0 Solving -2 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -0.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5x + x2 = 0 + 1 -0.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5x + x2 = 1 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5x + x2 = 1.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + -0.25) equal to 1.030776406 and -1.030776406.

Subproblem 1

x + -0.25 = 1.030776406 Simplifying x + -0.25 = 1.030776406 Reorder the terms: -0.25 + x = 1.030776406 Solving -0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.030776406 + 0.25 x = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 x = 1.280776406 Simplifying x = 1.280776406

Subproblem 2

x + -0.25 = -1.030776406 Simplifying x + -0.25 = -1.030776406 Reorder the terms: -0.25 + x = -1.030776406 Solving -0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.030776406 + 0.25 x = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 x = -0.780776406 Simplifying x = -0.780776406

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.280776406, -0.780776406}

Solution

x = {1.280776406, -0.780776406}

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