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Simplifying x2 + 13x + -180 = 0 Reorder the terms: -180 + 13x + x2 = 0 Solving -180 + 13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 13x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 13x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 13x + x2 = 0 + 180 13x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 13x + x2 = 180 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 = 180 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 180 + 42.25 Combine like terms: 180 + 42.25 = 222.25 42.25 + 13x + x2 = 222.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + 6.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + 6.5 = 14.908051516 Simplifying x + 6.5 = 14.908051516 Reorder the terms: 6.5 + x = 14.908051516 Solving 6.5 + x = 14.908051516 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 = 14.908051516 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 14.908051516 + -6.5 x = 14.908051516 + -6.5 Combine like terms: 14.908051516 + -6.5 = 8.408051516 x = 8.408051516 Simplifying x = 8.408051516Subproblem 2
x + 6.5 = -14.908051516 Simplifying x + 6.5 = -14.908051516 Reorder the terms: 6.5 + x = -14.908051516 Solving 6.5 + x = -14.908051516 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 = -14.908051516 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -14.908051516 + -6.5 x = -14.908051516 + -6.5 Combine like terms: -14.908051516 + -6.5 = -21.408051516 x = -21.408051516 Simplifying x = -21.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.408051516, -21.408051516}
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