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Simplifying x2 + -3x + -64 = 0 Reorder the terms: -64 + -3x + x2 = 0 Solving -64 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -3x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -3x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -3x + x2 = 0 + 64 -3x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -3x + x2 = 64 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 = 64 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 64 + 2.25 Combine like terms: 64 + 2.25 = 66.25 2.25 + -3x + x2 = 66.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -1.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -1.5 = 8.139410298 Simplifying x + -1.5 = 8.139410298 Reorder the terms: -1.5 + x = 8.139410298 Solving -1.5 + x = 8.139410298 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 = 8.139410298 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.139410298 + 1.5 x = 8.139410298 + 1.5 Combine like terms: 8.139410298 + 1.5 = 9.639410298 x = 9.639410298 Simplifying x = 9.639410298Subproblem 2
x + -1.5 = -8.139410298 Simplifying x + -1.5 = -8.139410298 Reorder the terms: -1.5 + x = -8.139410298 Solving -1.5 + x = -8.139410298 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 = -8.139410298 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.139410298 + 1.5 x = -8.139410298 + 1.5 Combine like terms: -8.139410298 + 1.5 = -6.639410298 x = -6.639410298 Simplifying x = -6.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.639410298, -6.639410298}
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