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Simplifying 48 = -16x2 + 48x + 864 Reorder the terms: 48 = 864 + 48x + -16x2 Solving 48 = 864 + 48x + -16x2 Solving for variable 'x'. Combine like terms: 48 + -864 = -816 -816 + -48x + 16x2 = 864 + 48x + -16x2 + -864 + -48x + 16x2 Reorder the terms: -816 + -48x + 16x2 = 864 + -864 + 48x + -48x + -16x2 + 16x2 Combine like terms: 864 + -864 = 0 -816 + -48x + 16x2 = 0 + 48x + -48x + -16x2 + 16x2 -816 + -48x + 16x2 = 48x + -48x + -16x2 + 16x2 Combine like terms: 48x + -48x = 0 -816 + -48x + 16x2 = 0 + -16x2 + 16x2 -816 + -48x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -816 + -48x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-51 + -3x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-51 + -3x + x2)' equal to zero and attempt to solve: Simplifying -51 + -3x + x2 = 0 Solving -51 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -3x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -3x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -3x + x2 = 0 + 51 -3x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -3x + x2 = 51 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 51 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 51 + 2.25 Combine like terms: 51 + 2.25 = 53.25 2.25 + -3x + x2 = 53.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 53.25 Calculate the square root of the right side: 7.29725976 Break this problem into two subproblems by setting (x + -1.5) equal to 7.29725976 and -7.29725976.Subproblem 1
x + -1.5 = 7.29725976 Simplifying x + -1.5 = 7.29725976 Reorder the terms: -1.5 + x = 7.29725976 Solving -1.5 + x = 7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 7.29725976 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 7.29725976 + 1.5 x = 7.29725976 + 1.5 Combine like terms: 7.29725976 + 1.5 = 8.79725976 x = 8.79725976 Simplifying x = 8.79725976Subproblem 2
x + -1.5 = -7.29725976 Simplifying x + -1.5 = -7.29725976 Reorder the terms: -1.5 + x = -7.29725976 Solving -1.5 + x = -7.29725976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -7.29725976 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -7.29725976 + 1.5 x = -7.29725976 + 1.5 Combine like terms: -7.29725976 + 1.5 = -5.79725976 x = -5.79725976 Simplifying x = -5.79725976Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.79725976, -5.79725976}Solution
x = {8.79725976, -5.79725976}
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