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Simplifying 300x + -0.10x2 + -125000 = 0 Reorder the terms: -125000 + 300x + -0.10x2 = 0 Solving -125000 + 300x + -0.10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.10 the coefficient of the squared term: Divide each side by '-0.10'. 1250000 + -3000x + x2 = 0 Move the constant term to the right: Add '-1250000' to each side of the equation. 1250000 + -3000x + -1250000 + x2 = 0 + -1250000 Reorder the terms: 1250000 + -1250000 + -3000x + x2 = 0 + -1250000 Combine like terms: 1250000 + -1250000 = 0 0 + -3000x + x2 = 0 + -1250000 -3000x + x2 = 0 + -1250000 Combine like terms: 0 + -1250000 = -1250000 -3000x + x2 = -1250000 The x term is -3000x. Take half its coefficient (-1500). Square it (2250000) and add it to both sides. Add '2250000' to each side of the equation. -3000x + 2250000 + x2 = -1250000 + 2250000 Reorder the terms: 2250000 + -3000x + x2 = -1250000 + 2250000 Combine like terms: -1250000 + 2250000 = 1000000 2250000 + -3000x + x2 = 1000000 Factor a perfect square on the left side: (x + -1500)(x + -1500) = 1000000 Calculate the square root of the right side: 1000 Break this problem into two subproblems by setting (x + -1500) equal to 1000 and -1000.Subproblem 1
x + -1500 = 1000 Simplifying x + -1500 = 1000 Reorder the terms: -1500 + x = 1000 Solving -1500 + x = 1000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + x = 1000 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = 1000 + 1500 x = 1000 + 1500 Combine like terms: 1000 + 1500 = 2500 x = 2500 Simplifying x = 2500Subproblem 2
x + -1500 = -1000 Simplifying x + -1500 = -1000 Reorder the terms: -1500 + x = -1000 Solving -1500 + x = -1000 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1500' to each side of the equation. -1500 + 1500 + x = -1000 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = -1000 + 1500 x = -1000 + 1500 Combine like terms: -1000 + 1500 = 500 x = 500 Simplifying x = 500Solution
The solution to the problem is based on the solutions from the subproblems. x = {2500, 500}
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