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Simplifying 2 = -16x2 + 60x + 120 Reorder the terms: 2 = 120 + 60x + -16x2 Solving 2 = 120 + 60x + -16x2 Solving for variable 'x'. Combine like terms: 2 + -120 = -118 -118 + -60x + 16x2 = 120 + 60x + -16x2 + -120 + -60x + 16x2 Reorder the terms: -118 + -60x + 16x2 = 120 + -120 + 60x + -60x + -16x2 + 16x2 Combine like terms: 120 + -120 = 0 -118 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2 -118 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2 Combine like terms: 60x + -60x = 0 -118 + -60x + 16x2 = 0 + -16x2 + 16x2 -118 + -60x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -118 + -60x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-59 + -30x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-59 + -30x + 8x2)' equal to zero and attempt to solve: Simplifying -59 + -30x + 8x2 = 0 Solving -59 + -30x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -7.375 + -3.75x + x2 = 0 Move the constant term to the right: Add '7.375' to each side of the equation. -7.375 + -3.75x + 7.375 + x2 = 0 + 7.375 Reorder the terms: -7.375 + 7.375 + -3.75x + x2 = 0 + 7.375 Combine like terms: -7.375 + 7.375 = 0.000 0.000 + -3.75x + x2 = 0 + 7.375 -3.75x + x2 = 0 + 7.375 Combine like terms: 0 + 7.375 = 7.375 -3.75x + x2 = 7.375 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 7.375 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 7.375 + 3.515625 Combine like terms: 7.375 + 3.515625 = 10.890625 3.515625 + -3.75x + x2 = 10.890625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + -1.875) equal to 3.300094696 and -3.300094696.Subproblem 1
x + -1.875 = 3.300094696 Simplifying x + -1.875 = 3.300094696 Reorder the terms: -1.875 + x = 3.300094696 Solving -1.875 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 3.300094696 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 3.300094696 + 1.875 x = 3.300094696 + 1.875 Combine like terms: 3.300094696 + 1.875 = 5.175094696 x = 5.175094696 Simplifying x = 5.175094696Subproblem 2
x + -1.875 = -3.300094696 Simplifying x + -1.875 = -3.300094696 Reorder the terms: -1.875 + x = -3.300094696 Solving -1.875 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -3.300094696 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -3.300094696 + 1.875 x = -3.300094696 + 1.875 Combine like terms: -3.300094696 + 1.875 = -1.425094696 x = -1.425094696 Simplifying x = -1.425094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.175094696, -1.425094696}Solution
x = {5.175094696, -1.425094696}
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