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Simplifying 150 = -16x2 + 80x + 96 Reorder the terms: 150 = 96 + 80x + -16x2 Solving 150 = 96 + 80x + -16x2 Solving for variable 'x'. Combine like terms: 150 + -96 = 54 54 + -80x + 16x2 = 96 + 80x + -16x2 + -96 + -80x + 16x2 Reorder the terms: 54 + -80x + 16x2 = 96 + -96 + 80x + -80x + -16x2 + 16x2 Combine like terms: 96 + -96 = 0 54 + -80x + 16x2 = 0 + 80x + -80x + -16x2 + 16x2 54 + -80x + 16x2 = 80x + -80x + -16x2 + 16x2 Combine like terms: 80x + -80x = 0 54 + -80x + 16x2 = 0 + -16x2 + 16x2 54 + -80x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 54 + -80x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + -40x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + -40x + 8x2)' equal to zero and attempt to solve: Simplifying 27 + -40x + 8x2 = 0 Solving 27 + -40x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.375 + -5x + x2 = 0 Move the constant term to the right: Add '-3.375' to each side of the equation. 3.375 + -5x + -3.375 + x2 = 0 + -3.375 Reorder the terms: 3.375 + -3.375 + -5x + x2 = 0 + -3.375 Combine like terms: 3.375 + -3.375 = 0.000 0.000 + -5x + x2 = 0 + -3.375 -5x + x2 = 0 + -3.375 Combine like terms: 0 + -3.375 = -3.375 -5x + x2 = -3.375 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 = -3.375 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3.375 + 6.25 Combine like terms: -3.375 + 6.25 = 2.875 6.25 + -5x + x2 = 2.875 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -2.5) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -2.5 = 1.695582496 Simplifying x + -2.5 = 1.695582496 Reorder the terms: -2.5 + x = 1.695582496 Solving -2.5 + x = 1.695582496 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 = 1.695582496 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.695582496 + 2.5 x = 1.695582496 + 2.5 Combine like terms: 1.695582496 + 2.5 = 4.195582496 x = 4.195582496 Simplifying x = 4.195582496Subproblem 2
x + -2.5 = -1.695582496 Simplifying x + -2.5 = -1.695582496 Reorder the terms: -2.5 + x = -1.695582496 Solving -2.5 + x = -1.695582496 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 = -1.695582496 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.695582496 + 2.5 x = -1.695582496 + 2.5 Combine like terms: -1.695582496 + 2.5 = 0.804417504 x = 0.804417504 Simplifying x = 0.804417504Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.195582496, 0.804417504}Solution
x = {4.195582496, 0.804417504}
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