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Simplifying 0 = 2x2 + 615x + -40500 Reorder the terms: 0 = -40500 + 615x + 2x2 Solving 0 = -40500 + 615x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 40500 = 40500 40500 + -615x + -2x2 = -40500 + 615x + 2x2 + 40500 + -615x + -2x2 Reorder the terms: 40500 + -615x + -2x2 = -40500 + 40500 + 615x + -615x + 2x2 + -2x2 Combine like terms: -40500 + 40500 = 0 40500 + -615x + -2x2 = 0 + 615x + -615x + 2x2 + -2x2 40500 + -615x + -2x2 = 615x + -615x + 2x2 + -2x2 Combine like terms: 615x + -615x = 0 40500 + -615x + -2x2 = 0 + 2x2 + -2x2 40500 + -615x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 40500 + -615x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -20250 + 307.5x + x2 = 0 Move the constant term to the right: Add '20250' to each side of the equation. -20250 + 307.5x + 20250 + x2 = 0 + 20250 Reorder the terms: -20250 + 20250 + 307.5x + x2 = 0 + 20250 Combine like terms: -20250 + 20250 = 0 0 + 307.5x + x2 = 0 + 20250 307.5x + x2 = 0 + 20250 Combine like terms: 0 + 20250 = 20250 307.5x + x2 = 20250 The x term is 307.5x. Take half its coefficient (153.75). Square it (23639.0625) and add it to both sides. Add '23639.0625' to each side of the equation. 307.5x + 23639.0625 + x2 = 20250 + 23639.0625 Reorder the terms: 23639.0625 + 307.5x + x2 = 20250 + 23639.0625 Combine like terms: 20250 + 23639.0625 = 43889.0625 23639.0625 + 307.5x + x2 = 43889.0625 Factor a perfect square on the left side: (x + 153.75)(x + 153.75) = 43889.0625 Calculate the square root of the right side: 209.497165852 Break this problem into two subproblems by setting (x + 153.75) equal to 209.497165852 and -209.497165852.Subproblem 1
x + 153.75 = 209.497165852 Simplifying x + 153.75 = 209.497165852 Reorder the terms: 153.75 + x = 209.497165852 Solving 153.75 + x = 209.497165852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-153.75' to each side of the equation. 153.75 + -153.75 + x = 209.497165852 + -153.75 Combine like terms: 153.75 + -153.75 = 0.00 0.00 + x = 209.497165852 + -153.75 x = 209.497165852 + -153.75 Combine like terms: 209.497165852 + -153.75 = 55.747165852 x = 55.747165852 Simplifying x = 55.747165852Subproblem 2
x + 153.75 = -209.497165852 Simplifying x + 153.75 = -209.497165852 Reorder the terms: 153.75 + x = -209.497165852 Solving 153.75 + x = -209.497165852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-153.75' to each side of the equation. 153.75 + -153.75 + x = -209.497165852 + -153.75 Combine like terms: 153.75 + -153.75 = 0.00 0.00 + x = -209.497165852 + -153.75 x = -209.497165852 + -153.75 Combine like terms: -209.497165852 + -153.75 = -363.247165852 x = -363.247165852 Simplifying x = -363.247165852Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.747165852, -363.247165852}
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