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Simplifying 10x2 + -36x + 144 = 2704 Reorder the terms: 144 + -36x + 10x2 = 2704 Solving 144 + -36x + 10x2 = 2704 Solving for variable 'x'. Reorder the terms: 144 + -2704 + -36x + 10x2 = 2704 + -2704 Combine like terms: 144 + -2704 = -2560 -2560 + -36x + 10x2 = 2704 + -2704 Combine like terms: 2704 + -2704 = 0 -2560 + -36x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1280 + -18x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1280 + -18x + 5x2)' equal to zero and attempt to solve: Simplifying -1280 + -18x + 5x2 = 0 Solving -1280 + -18x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -256 + -3.6x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + -3.6x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + -3.6x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + -3.6x + x2 = 0 + 256 -3.6x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 -3.6x + x2 = 256 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = 256 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = 256 + 3.24 Combine like terms: 256 + 3.24 = 259.24 3.24 + -3.6x + x2 = 259.24 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 259.24 Calculate the square root of the right side: 16.10093165 Break this problem into two subproblems by setting (x + -1.8) equal to 16.10093165 and -16.10093165.Subproblem 1
x + -1.8 = 16.10093165 Simplifying x + -1.8 = 16.10093165 Reorder the terms: -1.8 + x = 16.10093165 Solving -1.8 + x = 16.10093165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 16.10093165 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 16.10093165 + 1.8 x = 16.10093165 + 1.8 Combine like terms: 16.10093165 + 1.8 = 17.90093165 x = 17.90093165 Simplifying x = 17.90093165Subproblem 2
x + -1.8 = -16.10093165 Simplifying x + -1.8 = -16.10093165 Reorder the terms: -1.8 + x = -16.10093165 Solving -1.8 + x = -16.10093165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -16.10093165 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -16.10093165 + 1.8 x = -16.10093165 + 1.8 Combine like terms: -16.10093165 + 1.8 = -14.30093165 x = -14.30093165 Simplifying x = -14.30093165Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.90093165, -14.30093165}Solution
x = {17.90093165, -14.30093165}
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