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Simplifying 832x + -148(9 + -294x)(41 + -42x) = -5492x(8 + -159)(414 + -245)(523 + -145) Multiply (9 + -294x) * (41 + -42x) 832x + -148(9(41 + -42x) + -294x * (41 + -42x)) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + -148((41 * 9 + -42x * 9) + -294x * (41 + -42x)) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + -148((369 + -378x) + -294x * (41 + -42x)) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + -148(369 + -378x + (41 * -294x + -42x * -294x)) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + -148(369 + -378x + (-12054x + 12348x2)) = -5492x(8 + -159)(414 + -245)(523 + -145) Combine like terms: -378x + -12054x = -12432x 832x + -148(369 + -12432x + 12348x2) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + (369 * -148 + -12432x * -148 + 12348x2 * -148) = -5492x(8 + -159)(414 + -245)(523 + -145) 832x + (-54612 + 1839936x + -1827504x2) = -5492x(8 + -159)(414 + -245)(523 + -145) Reorder the terms: -54612 + 832x + 1839936x + -1827504x2 = -5492x(8 + -159)(414 + -245)(523 + -145) Combine like terms: 832x + 1839936x = 1840768x -54612 + 1840768x + -1827504x2 = -5492x(8 + -159)(414 + -245)(523 + -145) Combine like terms: 8 + -159 = -151 -54612 + 1840768x + -1827504x2 = -5492x(-151)(414 + -245)(523 + -145) Combine like terms: 414 + -245 = 169 -54612 + 1840768x + -1827504x2 = -5492x * -151(169)(523 + -145) Combine like terms: 523 + -145 = 378 -54612 + 1840768x + -1827504x2 = -5492x * -151 * 169(378) Reorder the terms for easier multiplication: -54612 + 1840768x + -1827504x2 = -5492 * -151 * 169 * 378x Multiply -5492 * -151 -54612 + 1840768x + -1827504x2 = 829292 * 169 * 378x Multiply 829292 * 169 -54612 + 1840768x + -1827504x2 = 140150348 * 378x Multiply 140150348 * 378 -54612 + 1840768x + -1827504x2 = 52976831540x Solving -54612 + 1840768x + -1827504x2 = 52976831540x Solving for variable 'x'. Reorder the terms: -54612 + 1840768x + -52976831540x + -1827504x2 = 52976831540x + -52976831540x Combine like terms: 1840768x + -52976831540x = -52974990772x -54612 + -52974990772x + -1827504x2 = 52976831540x + -52976831540x Combine like terms: 52976831540x + -52976831540x = 0 -54612 + -52974990772x + -1827504x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(13653 + 13243747690x + 456876x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(13653 + 13243747690x + 456876x2)' equal to zero and attempt to solve: Simplifying 13653 + 13243747690x + 456876x2 = 0 Solving 13653 + 13243747690x + 456876x2 = 0 Begin completing the square. Divide all terms by 456876 the coefficient of the squared term: Divide each side by '456876'. 0.02988338192 + 28987.61959x + x2 = 0 Move the constant term to the right: Add '-0.02988338192' to each side of the equation. 0.02988338192 + 28987.61959x + -0.02988338192 + x2 = 0 + -0.02988338192 Reorder the terms: 0.02988338192 + -0.02988338192 + 28987.61959x + x2 = 0 + -0.02988338192 Combine like terms: 0.02988338192 + -0.02988338192 = 0.00000000000 0.00000000000 + 28987.61959x + x2 = 0 + -0.02988338192 28987.61959x + x2 = 0 + -0.02988338192 Combine like terms: 0 + -0.02988338192 = -0.02988338192 28987.61959x + x2 = -0.02988338192 The x term is 28987.61959x. Take half its coefficient (14493.8098). Square it (210070522.5) and add it to both sides. Add '210070522.5' to each side of the equation. 28987.61959x + 210070522.5 + x2 = -0.02988338192 + 210070522.5 Reorder the terms: 210070522.5 + 28987.61959x + x2 = -0.02988338192 + 210070522.5 Combine like terms: -0.02988338192 + 210070522.5 = 210070522.47011661808 210070522.5 + 28987.61959x + x2 = 210070522.47011661808 Factor a perfect square on the left side: (x + 14493.8098)(x + 14493.8098) = 210070522.47011661808 Calculate the square root of the right side: 14493.809798328 Break this problem into two subproblems by setting (x + 14493.8098) equal to 14493.809798328 and -14493.809798328.Subproblem 1
x + 14493.8098 = 14493.809798328 Simplifying x + 14493.8098 = 14493.809798328 Reorder the terms: 14493.8098 + x = 14493.809798328 Solving 14493.8098 + x = 14493.809798328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14493.8098' to each side of the equation. 14493.8098 + -14493.8098 + x = 14493.809798328 + -14493.8098 Combine like terms: 14493.8098 + -14493.8098 = 0.0000 0.0000 + x = 14493.809798328 + -14493.8098 x = 14493.809798328 + -14493.8098 Combine like terms: 14493.809798328 + -14493.8098 = -0.000001672 x = -0.000001672 Simplifying x = -0.000001672Subproblem 2
x + 14493.8098 = -14493.809798328 Simplifying x + 14493.8098 = -14493.809798328 Reorder the terms: 14493.8098 + x = -14493.809798328 Solving 14493.8098 + x = -14493.809798328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14493.8098' to each side of the equation. 14493.8098 + -14493.8098 + x = -14493.809798328 + -14493.8098 Combine like terms: 14493.8098 + -14493.8098 = 0.0000 0.0000 + x = -14493.809798328 + -14493.8098 x = -14493.809798328 + -14493.8098 Combine like terms: -14493.809798328 + -14493.8098 = -28987.619598328 x = -28987.619598328 Simplifying x = -28987.619598328Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.000001672, -28987.619598328}Solution
x = {-0.000001672, -28987.619598328}
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