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Simplifying x2 + 19x + 24 = 0 Reorder the terms: 24 + 19x + x2 = 0 Solving 24 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 19x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 19x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 19x + x2 = 0 + -24 19x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 19x + x2 = -24 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -24 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -24 + 90.25 Combine like terms: -24 + 90.25 = 66.25 90.25 + 19x + x2 = 66.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (x + 9.5) equal to 8.139410298 and -8.139410298.Subproblem 1
x + 9.5 = 8.139410298 Simplifying x + 9.5 = 8.139410298 Reorder the terms: 9.5 + x = 8.139410298 Solving 9.5 + x = 8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 8.139410298 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.139410298 + -9.5 x = 8.139410298 + -9.5 Combine like terms: 8.139410298 + -9.5 = -1.360589702 x = -1.360589702 Simplifying x = -1.360589702Subproblem 2
x + 9.5 = -8.139410298 Simplifying x + 9.5 = -8.139410298 Reorder the terms: 9.5 + x = -8.139410298 Solving 9.5 + x = -8.139410298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -8.139410298 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.139410298 + -9.5 x = -8.139410298 + -9.5 Combine like terms: -8.139410298 + -9.5 = -17.639410298 x = -17.639410298 Simplifying x = -17.639410298Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.360589702, -17.639410298}
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