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Simplifying (x + 3)(x + -2) = 60 Reorder the terms: (3 + x)(x + -2) = 60 Reorder the terms: (3 + x)(-2 + x) = 60 Multiply (3 + x) * (-2 + x) (3(-2 + x) + x(-2 + x)) = 60 ((-2 * 3 + x * 3) + x(-2 + x)) = 60 ((-6 + 3x) + x(-2 + x)) = 60 (-6 + 3x + (-2 * x + x * x)) = 60 (-6 + 3x + (-2x + x2)) = 60 Combine like terms: 3x + -2x = 1x (-6 + 1x + x2) = 60 Solving -6 + 1x + x2 = 60 Solving for variable 'x'. Reorder the terms: -6 + -60 + 1x + x2 = 60 + -60 Combine like terms: -6 + -60 = -66 -66 + 1x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -66 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 1x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 1x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 1x + x2 = 0 + 66 1x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 1x + x2 = 66 The x term is 1x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 66 + 0.25 Reorder the terms: 0.25 + x + x2 = 66 + 0.25 Combine like terms: 66 + 0.25 = 66.25 0.25 + x + x2 = 66.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + 0.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + 0.5 = 8.139410298 Simplifying x + 0.5 = 8.139410298 Reorder the terms: 0.5 + x = 8.139410298 Solving 0.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.139410298 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.139410298 + -0.5 x = 8.139410298 + -0.5 Combine like terms: 8.139410298 + -0.5 = 7.639410298 x = 7.639410298 Simplifying x = 7.639410298Subproblem 2
x + 0.5 = -8.139410298 Simplifying x + 0.5 = -8.139410298 Reorder the terms: 0.5 + x = -8.139410298 Solving 0.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.139410298 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.139410298 + -0.5 x = -8.139410298 + -0.5 Combine like terms: -8.139410298 + -0.5 = -8.639410298 x = -8.639410298 Simplifying x = -8.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.639410298, -8.639410298}
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