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Simplifying 20x = 20 + -16x2 + 32x Reorder the terms: 20x = 20 + 32x + -16x2 Solving 20x = 20 + 32x + -16x2 Solving for variable 'x'. Reorder the terms: -20 + 20x + -32x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2 Combine like terms: 20x + -32x = -12x -20 + -12x + 16x2 = 20 + 32x + -16x2 + -20 + -32x + 16x2 Reorder the terms: -20 + -12x + 16x2 = 20 + -20 + 32x + -32x + -16x2 + 16x2 Combine like terms: 20 + -20 = 0 -20 + -12x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -20 + -12x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -20 + -12x + 16x2 = 0 + -16x2 + 16x2 -20 + -12x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -20 + -12x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + -3x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + -3x + 4x2 = 0 Solving -5 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -0.75x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -0.75x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -0.75x + x2 = 0 + 1.25 -0.75x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -0.75x + x2 = 1.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 1.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.25 + 0.140625 Combine like terms: 1.25 + 0.140625 = 1.390625 0.140625 + -0.75x + x2 = 1.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -0.375) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -0.375 = 1.179247642 Simplifying x + -0.375 = 1.179247642 Reorder the terms: -0.375 + x = 1.179247642 Solving -0.375 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.179247642 + 0.375 x = 1.179247642 + 0.375 Combine like terms: 1.179247642 + 0.375 = 1.554247642 x = 1.554247642 Simplifying x = 1.554247642Subproblem 2
x + -0.375 = -1.179247642 Simplifying x + -0.375 = -1.179247642 Reorder the terms: -0.375 + x = -1.179247642 Solving -0.375 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.179247642 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.179247642 + 0.375 x = -1.179247642 + 0.375 Combine like terms: -1.179247642 + 0.375 = -0.804247642 x = -0.804247642 Simplifying x = -0.804247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.554247642, -0.804247642}Solution
x = {1.554247642, -0.804247642}
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