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Simplifying x2 + 15x + 36 = 180 Reorder the terms: 36 + 15x + x2 = 180 Solving 36 + 15x + x2 = 180 Solving for variable 'x'. Reorder the terms: 36 + -180 + 15x + x2 = 180 + -180 Combine like terms: 36 + -180 = -144 -144 + 15x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -144 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 15x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 15x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 15x + x2 = 0 + 144 15x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 15x + x2 = 144 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 144 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 144 + 56.25 Combine like terms: 144 + 56.25 = 200.25 56.25 + 15x + x2 = 200.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 7.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 7.5 = 14.150971698 Simplifying x + 7.5 = 14.150971698 Reorder the terms: 7.5 + x = 14.150971698 Solving 7.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 14.150971698 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 14.150971698 + -7.5 x = 14.150971698 + -7.5 Combine like terms: 14.150971698 + -7.5 = 6.650971698 x = 6.650971698 Simplifying x = 6.650971698Subproblem 2
x + 7.5 = -14.150971698 Simplifying x + 7.5 = -14.150971698 Reorder the terms: 7.5 + x = -14.150971698 Solving 7.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -14.150971698 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -14.150971698 + -7.5 x = -14.150971698 + -7.5 Combine like terms: -14.150971698 + -7.5 = -21.650971698 x = -21.650971698 Simplifying x = -21.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.650971698, -21.650971698}
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