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Simplifying 80 = -16x2 + 80x + 96 Reorder the terms: 80 = 96 + 80x + -16x2 Solving 80 = 96 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 80 + -96 = -16 -16 + -80x + 16x2 = 96 + 80x + -16x2 + -96 + -80x + 16x2 Reorder the terms: -16 + -80x + 16x2 = 96 + -96 + 80x + -80x + -16x2 + 16x2 Combine like terms: 96 + -96 = 0 -16 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 -16 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 -16 + -80x + 16x2 = 0 + -16x2 + 16x2 -16 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -16 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-1 + -5x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + -5x + x2)' equal to zero and attempt to solve: Simplifying -1 + -5x + x2 = 0 Solving -1 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x + x2 = 0 + 1 -5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -5x + x2 = 1 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 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + -5x + x2 = 7.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + -2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + -2.5 = 2.692582404 Simplifying x + -2.5 = 2.692582404 Reorder the terms: -2.5 + x = 2.692582404 Solving -2.5 + x = 2.692582404 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 = 2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.692582404 + 2.5 x = 2.692582404 + 2.5 Combine like terms: 2.692582404 + 2.5 = 5.192582404 x = 5.192582404 Simplifying x = 5.192582404Subproblem 2
x + -2.5 = -2.692582404 Simplifying x + -2.5 = -2.692582404 Reorder the terms: -2.5 + x = -2.692582404 Solving -2.5 + x = -2.692582404 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 = -2.692582404 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.692582404 + 2.5 x = -2.692582404 + 2.5 Combine like terms: -2.692582404 + 2.5 = -0.192582404 x = -0.192582404 Simplifying x = -0.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.192582404, -0.192582404}Solution
x = {5.192582404, -0.192582404}
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