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Simplifying 15x + x2 + -24 = 180 Reorder the terms: -24 + 15x + x2 = 180 Solving -24 + 15x + x2 = 180 Solving for variable 'x'. Reorder the terms: -24 + -180 + 15x + x2 = 180 + -180 Combine like terms: -24 + -180 = -204 -204 + 15x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -204 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + 15x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 15x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 15x + x2 = 0 + 204 15x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 15x + x2 = 204 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 = 204 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 204 + 56.25 Combine like terms: 204 + 56.25 = 260.25 56.25 + 15x + x2 = 260.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 260.25 Calculate the square root of the right side: 16.132265805 Break this problem into two subproblems by setting (x + 7.5) equal to 16.132265805 and -16.132265805.Subproblem 1
x + 7.5 = 16.132265805 Simplifying x + 7.5 = 16.132265805 Reorder the terms: 7.5 + x = 16.132265805 Solving 7.5 + x = 16.132265805 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 = 16.132265805 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 16.132265805 + -7.5 x = 16.132265805 + -7.5 Combine like terms: 16.132265805 + -7.5 = 8.632265805 x = 8.632265805 Simplifying x = 8.632265805Subproblem 2
x + 7.5 = -16.132265805 Simplifying x + 7.5 = -16.132265805 Reorder the terms: 7.5 + x = -16.132265805 Solving 7.5 + x = -16.132265805 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 = -16.132265805 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -16.132265805 + -7.5 x = -16.132265805 + -7.5 Combine like terms: -16.132265805 + -7.5 = -23.632265805 x = -23.632265805 Simplifying x = -23.632265805Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.632265805, -23.632265805}
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