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Simplifying 0 = 4x2 + 20x + -20 Reorder the terms: 0 = -20 + 20x + 4x2 Solving 0 = -20 + 20x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 20 = 20 20 + -20x + -4x2 = -20 + 20x + 4x2 + 20 + -20x + -4x2 Reorder the terms: 20 + -20x + -4x2 = -20 + 20 + 20x + -20x + 4x2 + -4x2 Combine like terms: -20 + 20 = 0 20 + -20x + -4x2 = 0 + 20x + -20x + 4x2 + -4x2 20 + -20x + -4x2 = 20x + -20x + 4x2 + -4x2 Combine like terms: 20x + -20x = 0 20 + -20x + -4x2 = 0 + 4x2 + -4x2 20 + -20x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 20 + -20x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -5x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + -5x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + -1x2 = 0 Solving 5 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 5x + x2 = 0 + 5 5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 5x + x2 = 5 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 = 5 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 5 + 6.25 Combine like terms: 5 + 6.25 = 11.25 6.25 + 5x + x2 = 11.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 2.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 2.5 = 3.354101966 Simplifying x + 2.5 = 3.354101966 Reorder the terms: 2.5 + x = 3.354101966 Solving 2.5 + x = 3.354101966 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 = 3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.354101966 + -2.5 x = 3.354101966 + -2.5 Combine like terms: 3.354101966 + -2.5 = 0.854101966 x = 0.854101966 Simplifying x = 0.854101966Subproblem 2
x + 2.5 = -3.354101966 Simplifying x + 2.5 = -3.354101966 Reorder the terms: 2.5 + x = -3.354101966 Solving 2.5 + x = -3.354101966 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 = -3.354101966 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.354101966 + -2.5 x = -3.354101966 + -2.5 Combine like terms: -3.354101966 + -2.5 = -5.854101966 x = -5.854101966 Simplifying x = -5.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.854101966, -5.854101966}Solution
x = {0.854101966, -5.854101966}
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