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Simplifying 10 = -16x2 + 96x Reorder the terms: 10 = 96x + -16x2 Solving 10 = 96x + -16x2 Solving for variable 'x'. Reorder the terms: 10 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2 Combine like terms: 96x + -96x = 0 10 + -96x + 16x2 = 0 + -16x2 + 16x2 10 + -96x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 10 + -96x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -48x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -48x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -48x + 8x2 = 0 Solving 5 + -48x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -6x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -6x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -6x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -6x + x2 = 0 + -0.625 -6x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -6x + x2 = -0.625 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.625 + 9 Reorder the terms: 9 + -6x + x2 = -0.625 + 9 Combine like terms: -0.625 + 9 = 8.375 9 + -6x + x2 = 8.375 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.375 Calculate the square root of the right side: 2.893959226 Break this problem into two subproblems by setting (x + -3) equal to 2.893959226 and -2.893959226.Subproblem 1
x + -3 = 2.893959226 Simplifying x + -3 = 2.893959226 Reorder the terms: -3 + x = 2.893959226 Solving -3 + x = 2.893959226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.893959226 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.893959226 + 3 x = 2.893959226 + 3 Combine like terms: 2.893959226 + 3 = 5.893959226 x = 5.893959226 Simplifying x = 5.893959226Subproblem 2
x + -3 = -2.893959226 Simplifying x + -3 = -2.893959226 Reorder the terms: -3 + x = -2.893959226 Solving -3 + x = -2.893959226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.893959226 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.893959226 + 3 x = -2.893959226 + 3 Combine like terms: -2.893959226 + 3 = 0.106040774 x = 0.106040774 Simplifying x = 0.106040774Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.893959226, 0.106040774}Solution
x = {5.893959226, 0.106040774}
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