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Simplifying x2 + -5x + 24 = 180 Reorder the terms: 24 + -5x + x2 = 180 Solving 24 + -5x + x2 = 180 Solving for variable 'x'. Reorder the terms: 24 + -180 + -5x + x2 = 180 + -180 Combine like terms: 24 + -180 = -156 -156 + -5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -156 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '156' to each side of the equation. -156 + -5x + 156 + x2 = 0 + 156 Reorder the terms: -156 + 156 + -5x + x2 = 0 + 156 Combine like terms: -156 + 156 = 0 0 + -5x + x2 = 0 + 156 -5x + x2 = 0 + 156 Combine like terms: 0 + 156 = 156 -5x + x2 = 156 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 = 156 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 156 + 6.25 Combine like terms: 156 + 6.25 = 162.25 6.25 + -5x + x2 = 162.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + -2.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + -2.5 = 12.737739203 Simplifying x + -2.5 = 12.737739203 Reorder the terms: -2.5 + x = 12.737739203 Solving -2.5 + x = 12.737739203 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 = 12.737739203 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 12.737739203 + 2.5 x = 12.737739203 + 2.5 Combine like terms: 12.737739203 + 2.5 = 15.237739203 x = 15.237739203 Simplifying x = 15.237739203Subproblem 2
x + -2.5 = -12.737739203 Simplifying x + -2.5 = -12.737739203 Reorder the terms: -2.5 + x = -12.737739203 Solving -2.5 + x = -12.737739203 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 = -12.737739203 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -12.737739203 + 2.5 x = -12.737739203 + 2.5 Combine like terms: -12.737739203 + 2.5 = -10.237739203 x = -10.237739203 Simplifying x = -10.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.237739203, -10.237739203}
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