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Simplifying 0 = x2 + 155x + -576600 Reorder the terms: 0 = -576600 + 155x + x2 Solving 0 = -576600 + 155x + x2 Solving for variable 'x'. Combine like terms: 0 + 576600 = 576600 576600 + -155x + -1x2 = -576600 + 155x + x2 + 576600 + -155x + -1x2 Reorder the terms: 576600 + -155x + -1x2 = -576600 + 576600 + 155x + -155x + x2 + -1x2 Combine like terms: -576600 + 576600 = 0 576600 + -155x + -1x2 = 0 + 155x + -155x + x2 + -1x2 576600 + -155x + -1x2 = 155x + -155x + x2 + -1x2 Combine like terms: 155x + -155x = 0 576600 + -155x + -1x2 = 0 + x2 + -1x2 576600 + -155x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 576600 + -155x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -576600 + 155x + x2 = 0 Move the constant term to the right: Add '576600' to each side of the equation. -576600 + 155x + 576600 + x2 = 0 + 576600 Reorder the terms: -576600 + 576600 + 155x + x2 = 0 + 576600 Combine like terms: -576600 + 576600 = 0 0 + 155x + x2 = 0 + 576600 155x + x2 = 0 + 576600 Combine like terms: 0 + 576600 = 576600 155x + x2 = 576600 The x term is 155x. Take half its coefficient (77.5). Square it (6006.25) and add it to both sides. Add '6006.25' to each side of the equation. 155x + 6006.25 + x2 = 576600 + 6006.25 Reorder the terms: 6006.25 + 155x + x2 = 576600 + 6006.25 Combine like terms: 576600 + 6006.25 = 582606.25 6006.25 + 155x + x2 = 582606.25 Factor a perfect square on the left side: (x + 77.5)(x + 77.5) = 582606.25 Calculate the square root of the right side: 763.286479639 Break this problem into two subproblems by setting (x + 77.5) equal to 763.286479639 and -763.286479639.Subproblem 1
x + 77.5 = 763.286479639 Simplifying x + 77.5 = 763.286479639 Reorder the terms: 77.5 + x = 763.286479639 Solving 77.5 + x = 763.286479639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-77.5' to each side of the equation. 77.5 + -77.5 + x = 763.286479639 + -77.5 Combine like terms: 77.5 + -77.5 = 0.0 0.0 + x = 763.286479639 + -77.5 x = 763.286479639 + -77.5 Combine like terms: 763.286479639 + -77.5 = 685.786479639 x = 685.786479639 Simplifying x = 685.786479639Subproblem 2
x + 77.5 = -763.286479639 Simplifying x + 77.5 = -763.286479639 Reorder the terms: 77.5 + x = -763.286479639 Solving 77.5 + x = -763.286479639 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-77.5' to each side of the equation. 77.5 + -77.5 + x = -763.286479639 + -77.5 Combine like terms: 77.5 + -77.5 = 0.0 0.0 + x = -763.286479639 + -77.5 x = -763.286479639 + -77.5 Combine like terms: -763.286479639 + -77.5 = -840.786479639 x = -840.786479639 Simplifying x = -840.786479639Solution
The solution to the problem is based on the solutions from the subproblems. x = {685.786479639, -840.786479639}
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