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Simplifying -0.000012x2 + -0.018x + 300 = 0 Reorder the terms: 300 + -0.018x + -0.000012x2 = 0 Solving 300 + -0.018x + -0.000012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.000012 the coefficient of the squared term: Divide each side by '-0.000012'. -25000000 + 1500x + x2 = 0 Move the constant term to the right: Add '25000000' to each side of the equation. -25000000 + 1500x + 25000000 + x2 = 0 + 25000000 Reorder the terms: -25000000 + 25000000 + 1500x + x2 = 0 + 25000000 Combine like terms: -25000000 + 25000000 = 0 0 + 1500x + x2 = 0 + 25000000 1500x + x2 = 0 + 25000000 Combine like terms: 0 + 25000000 = 25000000 1500x + x2 = 25000000 The x term is 1500x. Take half its coefficient (750). Square it (562500) and add it to both sides. Add '562500' to each side of the equation. 1500x + 562500 + x2 = 25000000 + 562500 Reorder the terms: 562500 + 1500x + x2 = 25000000 + 562500 Combine like terms: 25000000 + 562500 = 25562500 562500 + 1500x + x2 = 25562500 Factor a perfect square on the left side: (x + 750)(x + 750) = 25562500 Calculate the square root of the right side: 5055.937104039 Break this problem into two subproblems by setting (x + 750) equal to 5055.937104039 and -5055.937104039.Subproblem 1
x + 750 = 5055.937104039 Simplifying x + 750 = 5055.937104039 Reorder the terms: 750 + x = 5055.937104039 Solving 750 + x = 5055.937104039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-750' to each side of the equation. 750 + -750 + x = 5055.937104039 + -750 Combine like terms: 750 + -750 = 0 0 + x = 5055.937104039 + -750 x = 5055.937104039 + -750 Combine like terms: 5055.937104039 + -750 = 4305.937104039 x = 4305.937104039 Simplifying x = 4305.937104039Subproblem 2
x + 750 = -5055.937104039 Simplifying x + 750 = -5055.937104039 Reorder the terms: 750 + x = -5055.937104039 Solving 750 + x = -5055.937104039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-750' to each side of the equation. 750 + -750 + x = -5055.937104039 + -750 Combine like terms: 750 + -750 = 0 0 + x = -5055.937104039 + -750 x = -5055.937104039 + -750 Combine like terms: -5055.937104039 + -750 = -5805.937104039 x = -5805.937104039 Simplifying x = -5805.937104039Solution
The solution to the problem is based on the solutions from the subproblems. x = {4305.937104039, -5805.937104039}
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