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Simplifying 180 = x2 + 5x + -36 Reorder the terms: 180 = -36 + 5x + x2 Solving 180 = -36 + 5x + x2 Solving for variable 'x'. Combine like terms: 180 + 36 = 216 216 + -5x + -1x2 = -36 + 5x + x2 + 36 + -5x + -1x2 Reorder the terms: 216 + -5x + -1x2 = -36 + 36 + 5x + -5x + x2 + -1x2 Combine like terms: -36 + 36 = 0 216 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 216 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 216 + -5x + -1x2 = 0 + x2 + -1x2 216 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 216 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -216 + 5x + x2 = 0 Move the constant term to the right: Add '216' to each side of the equation. -216 + 5x + 216 + x2 = 0 + 216 Reorder the terms: -216 + 216 + 5x + x2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 5x + x2 = 0 + 216 5x + x2 = 0 + 216 Combine like terms: 0 + 216 = 216 5x + x2 = 216 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 216 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 216 + 6.25 Combine like terms: 216 + 6.25 = 222.25 6.25 + 5x + x2 = 222.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + 2.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + 2.5 = 14.908051516 Simplifying x + 2.5 = 14.908051516 Reorder the terms: 2.5 + x = 14.908051516 Solving 2.5 + x = 14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 14.908051516 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 14.908051516 + -2.5 x = 14.908051516 + -2.5 Combine like terms: 14.908051516 + -2.5 = 12.408051516 x = 12.408051516 Simplifying x = 12.408051516Subproblem 2
x + 2.5 = -14.908051516 Simplifying x + 2.5 = -14.908051516 Reorder the terms: 2.5 + x = -14.908051516 Solving 2.5 + x = -14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -14.908051516 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -14.908051516 + -2.5 x = -14.908051516 + -2.5 Combine like terms: -14.908051516 + -2.5 = -17.408051516 x = -17.408051516 Simplifying x = -17.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.408051516, -17.408051516}
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