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Simplifying 180 = 1x2 + 19x + 48 Reorder the terms: 180 = 48 + 19x + 1x2 Solving 180 = 48 + 19x + 1x2 Solving for variable 'x'. Combine like terms: 180 + -48 = 132 132 + -19x + -1x2 = 48 + 19x + 1x2 + -48 + -19x + -1x2 Reorder the terms: 132 + -19x + -1x2 = 48 + -48 + 19x + -19x + 1x2 + -1x2 Combine like terms: 48 + -48 = 0 132 + -19x + -1x2 = 0 + 19x + -19x + 1x2 + -1x2 132 + -19x + -1x2 = 19x + -19x + 1x2 + -1x2 Combine like terms: 19x + -19x = 0 132 + -19x + -1x2 = 0 + 1x2 + -1x2 132 + -19x + -1x2 = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 132 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -132 + 19x + x2 = 0 Move the constant term to the right: Add '132' to each side of the equation. -132 + 19x + 132 + x2 = 0 + 132 Reorder the terms: -132 + 132 + 19x + x2 = 0 + 132 Combine like terms: -132 + 132 = 0 0 + 19x + x2 = 0 + 132 19x + x2 = 0 + 132 Combine like terms: 0 + 132 = 132 19x + x2 = 132 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 = 132 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 132 + 90.25 Combine like terms: 132 + 90.25 = 222.25 90.25 + 19x + x2 = 222.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 222.25 Calculate the square root of the right side: 14.908051516 Break this problem into two subproblems by setting (x + 9.5) equal to 14.908051516 and -14.908051516.Subproblem 1
x + 9.5 = 14.908051516 Simplifying x + 9.5 = 14.908051516 Reorder the terms: 9.5 + x = 14.908051516 Solving 9.5 + x = 14.908051516 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 = 14.908051516 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 14.908051516 + -9.5 x = 14.908051516 + -9.5 Combine like terms: 14.908051516 + -9.5 = 5.408051516 x = 5.408051516 Simplifying x = 5.408051516Subproblem 2
x + 9.5 = -14.908051516 Simplifying x + 9.5 = -14.908051516 Reorder the terms: 9.5 + x = -14.908051516 Solving 9.5 + x = -14.908051516 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 = -14.908051516 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -14.908051516 + -9.5 x = -14.908051516 + -9.5 Combine like terms: -14.908051516 + -9.5 = -24.408051516 x = -24.408051516 Simplifying x = -24.408051516Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.408051516, -24.408051516}
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