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Simplifying -0.004x2 + 32x + -150 = 0 Reorder the terms: -150 + 32x + -0.004x2 = 0 Solving -150 + 32x + -0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. 37500 + -8000x + x2 = 0 Move the constant term to the right: Add '-37500' to each side of the equation. 37500 + -8000x + -37500 + x2 = 0 + -37500 Reorder the terms: 37500 + -37500 + -8000x + x2 = 0 + -37500 Combine like terms: 37500 + -37500 = 0 0 + -8000x + x2 = 0 + -37500 -8000x + x2 = 0 + -37500 Combine like terms: 0 + -37500 = -37500 -8000x + x2 = -37500 The x term is -8000x. Take half its coefficient (-4000). Square it (16000000) and add it to both sides. Add '16000000' to each side of the equation. -8000x + 16000000 + x2 = -37500 + 16000000 Reorder the terms: 16000000 + -8000x + x2 = -37500 + 16000000 Combine like terms: -37500 + 16000000 = 15962500 16000000 + -8000x + x2 = 15962500 Factor a perfect square on the left side: (x + -4000)(x + -4000) = 15962500 Calculate the square root of the right side: 3995.309750195 Break this problem into two subproblems by setting (x + -4000) equal to 3995.309750195 and -3995.309750195.Subproblem 1
x + -4000 = 3995.309750195 Simplifying x + -4000 = 3995.309750195 Reorder the terms: -4000 + x = 3995.309750195 Solving -4000 + x = 3995.309750195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4000' to each side of the equation. -4000 + 4000 + x = 3995.309750195 + 4000 Combine like terms: -4000 + 4000 = 0 0 + x = 3995.309750195 + 4000 x = 3995.309750195 + 4000 Combine like terms: 3995.309750195 + 4000 = 7995.309750195 x = 7995.309750195 Simplifying x = 7995.309750195Subproblem 2
x + -4000 = -3995.309750195 Simplifying x + -4000 = -3995.309750195 Reorder the terms: -4000 + x = -3995.309750195 Solving -4000 + x = -3995.309750195 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4000' to each side of the equation. -4000 + 4000 + x = -3995.309750195 + 4000 Combine like terms: -4000 + 4000 = 0 0 + x = -3995.309750195 + 4000 x = -3995.309750195 + 4000 Combine like terms: -3995.309750195 + 4000 = 4.690249805 x = 4.690249805 Simplifying x = 4.690249805Solution
The solution to the problem is based on the solutions from the subproblems. x = {7995.309750195, 4.690249805}
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