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Simplifying 0 = 20 + 80x + -16x2 Solving 0 = 20 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -80x + 16x2 = 20 + 80x + -16x2 + -20 + -80x + 16x2 Reorder the terms: -20 + -80x + 16x2 = 20 + -20 + 80x + -80x + -16x2 + 16x2 Combine like terms: 20 + -20 = 0 -20 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 -20 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 -20 + -80x + 16x2 = 0 + -16x2 + 16x2 -20 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -20x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -20x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -20x + 4x2 = 0 Solving -5 + -20x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -5x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -5x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -5x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -5x + x2 = 0 + 1.25 -5x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -5x + x2 = 1.25 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 1.25 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1.25 + 6.25 Combine like terms: 1.25 + 6.25 = 7.5 6.25 + -5x + x2 = 7.5 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -2.5) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -2.5 = 2.738612788 Simplifying x + -2.5 = 2.738612788 Reorder the terms: -2.5 + x = 2.738612788 Solving -2.5 + x = 2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.738612788 + 2.5 x = 2.738612788 + 2.5 Combine like terms: 2.738612788 + 2.5 = 5.238612788 x = 5.238612788 Simplifying x = 5.238612788Subproblem 2
x + -2.5 = -2.738612788 Simplifying x + -2.5 = -2.738612788 Reorder the terms: -2.5 + x = -2.738612788 Solving -2.5 + x = -2.738612788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.738612788 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.738612788 + 2.5 x = -2.738612788 + 2.5 Combine like terms: -2.738612788 + 2.5 = -0.238612788 x = -0.238612788 Simplifying x = -0.238612788Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.238612788, -0.238612788}Solution
x = {5.238612788, -0.238612788}
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