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Simplifying 50 = -16x2 + -20x + 180 Reorder the terms: 50 = 180 + -20x + -16x2 Solving 50 = 180 + -20x + -16x2 Solving for variable 'x'. Combine like terms: 50 + -180 = -130 -130 + 20x + 16x2 = 180 + -20x + -16x2 + -180 + 20x + 16x2 Reorder the terms: -130 + 20x + 16x2 = 180 + -180 + -20x + 20x + -16x2 + 16x2 Combine like terms: 180 + -180 = 0 -130 + 20x + 16x2 = 0 + -20x + 20x + -16x2 + 16x2 -130 + 20x + 16x2 = -20x + 20x + -16x2 + 16x2 Combine like terms: -20x + 20x = 0 -130 + 20x + 16x2 = 0 + -16x2 + 16x2 -130 + 20x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -130 + 20x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-65 + 10x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-65 + 10x + 8x2)' equal to zero and attempt to solve: Simplifying -65 + 10x + 8x2 = 0 Solving -65 + 10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -8.125 + 1.25x + x2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 1.25x + 8.125 + x2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 1.25x + x2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 1.25x + x2 = 0 + 8.125 1.25x + x2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 1.25x + x2 = 8.125 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 8.125 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 8.125 + 0.390625 Combine like terms: 8.125 + 0.390625 = 8.515625 0.390625 + 1.25x + x2 = 8.515625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 8.515625 Calculate the square root of the right side: 2.918154382 Break this problem into two subproblems by setting (x + 0.625) equal to 2.918154382 and -2.918154382.Subproblem 1
x + 0.625 = 2.918154382 Simplifying x + 0.625 = 2.918154382 Reorder the terms: 0.625 + x = 2.918154382 Solving 0.625 + x = 2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 2.918154382 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 2.918154382 + -0.625 x = 2.918154382 + -0.625 Combine like terms: 2.918154382 + -0.625 = 2.293154382 x = 2.293154382 Simplifying x = 2.293154382Subproblem 2
x + 0.625 = -2.918154382 Simplifying x + 0.625 = -2.918154382 Reorder the terms: 0.625 + x = -2.918154382 Solving 0.625 + x = -2.918154382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -2.918154382 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -2.918154382 + -0.625 x = -2.918154382 + -0.625 Combine like terms: -2.918154382 + -0.625 = -3.543154382 x = -3.543154382 Simplifying x = -3.543154382Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.293154382, -3.543154382}Solution
x = {2.293154382, -3.543154382}
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