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Simplifying 0 = -0.004x2 + 12x + -1500 Reorder the terms: 0 = -1500 + 12x + -0.004x2 Solving 0 = -1500 + 12x + -0.004x2 Solving for variable 'x'. Combine like terms: 0 + 1500 = 1500 1500 + -12x + 0.004x2 = -1500 + 12x + -0.004x2 + 1500 + -12x + 0.004x2 Reorder the terms: 1500 + -12x + 0.004x2 = -1500 + 1500 + 12x + -12x + -0.004x2 + 0.004x2 Combine like terms: -1500 + 1500 = 0 1500 + -12x + 0.004x2 = 0 + 12x + -12x + -0.004x2 + 0.004x2 1500 + -12x + 0.004x2 = 12x + -12x + -0.004x2 + 0.004x2 Combine like terms: 12x + -12x = 0 1500 + -12x + 0.004x2 = 0 + -0.004x2 + 0.004x2 1500 + -12x + 0.004x2 = -0.004x2 + 0.004x2 Combine like terms: -0.004x2 + 0.004x2 = 0.000 1500 + -12x + 0.004x2 = 0.000 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. 375000 + -3000x + x2 = 0 Move the constant term to the right: Add '-375000' to each side of the equation. 375000 + -3000x + -375000 + x2 = 0 + -375000 Reorder the terms: 375000 + -375000 + -3000x + x2 = 0 + -375000 Combine like terms: 375000 + -375000 = 0 0 + -3000x + x2 = 0 + -375000 -3000x + x2 = 0 + -375000 Combine like terms: 0 + -375000 = -375000 -3000x + x2 = -375000 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 = -375000 + 2250000 Reorder the terms: 2250000 + -3000x + x2 = -375000 + 2250000 Combine like terms: -375000 + 2250000 = 1875000 2250000 + -3000x + x2 = 1875000 Factor a perfect square on the left side: (x + -1500)(x + -1500) = 1875000 Calculate the square root of the right side: 1369.306393763 Break this problem into two subproblems by setting (x + -1500) equal to 1369.306393763 and -1369.306393763.Subproblem 1
x + -1500 = 1369.306393763 Simplifying x + -1500 = 1369.306393763 Reorder the terms: -1500 + x = 1369.306393763 Solving -1500 + x = 1369.306393763 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 = 1369.306393763 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = 1369.306393763 + 1500 x = 1369.306393763 + 1500 Combine like terms: 1369.306393763 + 1500 = 2869.306393763 x = 2869.306393763 Simplifying x = 2869.306393763Subproblem 2
x + -1500 = -1369.306393763 Simplifying x + -1500 = -1369.306393763 Reorder the terms: -1500 + x = -1369.306393763 Solving -1500 + x = -1369.306393763 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 = -1369.306393763 + 1500 Combine like terms: -1500 + 1500 = 0 0 + x = -1369.306393763 + 1500 x = -1369.306393763 + 1500 Combine like terms: -1369.306393763 + 1500 = 130.693606237 x = 130.693606237 Simplifying x = 130.693606237Solution
The solution to the problem is based on the solutions from the subproblems. x = {2869.306393763, 130.693606237}
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