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Simplifying 50 = -16x2 + 16x + 60 Reorder the terms: 50 = 60 + 16x + -16x2 Solving 50 = 60 + 16x + -16x2 Solving for variable 'x'. Combine like terms: 50 + -60 = -10 -10 + -16x + 16x2 = 60 + 16x + -16x2 + -60 + -16x + 16x2 Reorder the terms: -10 + -16x + 16x2 = 60 + -60 + 16x + -16x + -16x2 + 16x2 Combine like terms: 60 + -60 = 0 -10 + -16x + 16x2 = 0 + 16x + -16x + -16x2 + 16x2 -10 + -16x + 16x2 = 16x + -16x + -16x2 + 16x2 Combine like terms: 16x + -16x = 0 -10 + -16x + 16x2 = 0 + -16x2 + 16x2 -10 + -16x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -10 + -16x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -8x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + -8x + 8x2 = 0 Solving -5 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -1x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1x + x2 = 0 + 0.625 -1x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1x + x2 = 0.625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 0.25 + -1x + x2 = 0.875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + -0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
x + -0.5 = 0.935414347 Simplifying x + -0.5 = 0.935414347 Reorder the terms: -0.5 + x = 0.935414347 Solving -0.5 + x = 0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.935414347 + 0.5 x = 0.935414347 + 0.5 Combine like terms: 0.935414347 + 0.5 = 1.435414347 x = 1.435414347 Simplifying x = 1.435414347Subproblem 2
x + -0.5 = -0.935414347 Simplifying x + -0.5 = -0.935414347 Reorder the terms: -0.5 + x = -0.935414347 Solving -0.5 + x = -0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.935414347 + 0.5 x = -0.935414347 + 0.5 Combine like terms: -0.935414347 + 0.5 = -0.435414347 x = -0.435414347 Simplifying x = -0.435414347Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435414347, -0.435414347}Solution
x = {1.435414347, -0.435414347}
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