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Simplifying 0 = -1x2 + 13x + 24 Reorder the terms: 0 = 24 + 13x + -1x2 Solving 0 = 24 + 13x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -13x + x2 = 24 + 13x + -1x2 + -24 + -13x + x2 Reorder the terms: -24 + -13x + x2 = 24 + -24 + 13x + -13x + -1x2 + x2 Combine like terms: 24 + -24 = 0 -24 + -13x + x2 = 0 + 13x + -13x + -1x2 + x2 -24 + -13x + x2 = 13x + -13x + -1x2 + x2 Combine like terms: 13x + -13x = 0 -24 + -13x + x2 = 0 + -1x2 + x2 -24 + -13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -24 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -13x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -13x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -13x + x2 = 0 + 24 -13x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -13x + x2 = 24 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 24 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 24 + 42.25 Combine like terms: 24 + 42.25 = 66.25 42.25 + -13x + x2 = 66.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + -6.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + -6.5 = 8.139410298 Simplifying x + -6.5 = 8.139410298 Reorder the terms: -6.5 + x = 8.139410298 Solving -6.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.139410298 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.139410298 + 6.5 x = 8.139410298 + 6.5 Combine like terms: 8.139410298 + 6.5 = 14.639410298 x = 14.639410298 Simplifying x = 14.639410298Subproblem 2
x + -6.5 = -8.139410298 Simplifying x + -6.5 = -8.139410298 Reorder the terms: -6.5 + x = -8.139410298 Solving -6.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.139410298 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.139410298 + 6.5 x = -8.139410298 + 6.5 Combine like terms: -8.139410298 + 6.5 = -1.639410298 x = -1.639410298 Simplifying x = -1.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.639410298, -1.639410298}
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