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Simplifying 0.49x2 + -6x + -5000 = 0 Reorder the terms: -5000 + -6x + 0.49x2 = 0 Solving -5000 + -6x + 0.49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.49 the coefficient of the squared term: Divide each side by '0.49'. -10204.08163 + -12.24489796x + x2 = 0 Move the constant term to the right: Add '10204.08163' to each side of the equation. -10204.08163 + -12.24489796x + 10204.08163 + x2 = 0 + 10204.08163 Reorder the terms: -10204.08163 + 10204.08163 + -12.24489796x + x2 = 0 + 10204.08163 Combine like terms: -10204.08163 + 10204.08163 = 0.00000 0.00000 + -12.24489796x + x2 = 0 + 10204.08163 -12.24489796x + x2 = 0 + 10204.08163 Combine like terms: 0 + 10204.08163 = 10204.08163 -12.24489796x + x2 = 10204.08163 The x term is -12.24489796x. Take half its coefficient (-6.12244898). Square it (37.48438151) and add it to both sides. Add '37.48438151' to each side of the equation. -12.24489796x + 37.48438151 + x2 = 10204.08163 + 37.48438151 Reorder the terms: 37.48438151 + -12.24489796x + x2 = 10204.08163 + 37.48438151 Combine like terms: 10204.08163 + 37.48438151 = 10241.56601151 37.48438151 + -12.24489796x + x2 = 10241.56601151 Factor a perfect square on the left side: (x + -6.12244898)(x + -6.12244898) = 10241.56601151 Calculate the square root of the right side: 101.200622585 Break this problem into two subproblems by setting (x + -6.12244898) equal to 101.200622585 and -101.200622585.Subproblem 1
x + -6.12244898 = 101.200622585 Simplifying x + -6.12244898 = 101.200622585 Reorder the terms: -6.12244898 + x = 101.200622585 Solving -6.12244898 + x = 101.200622585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + x = 101.200622585 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + x = 101.200622585 + 6.12244898 x = 101.200622585 + 6.12244898 Combine like terms: 101.200622585 + 6.12244898 = 107.323071565 x = 107.323071565 Simplifying x = 107.323071565Subproblem 2
x + -6.12244898 = -101.200622585 Simplifying x + -6.12244898 = -101.200622585 Reorder the terms: -6.12244898 + x = -101.200622585 Solving -6.12244898 + x = -101.200622585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12244898' to each side of the equation. -6.12244898 + 6.12244898 + x = -101.200622585 + 6.12244898 Combine like terms: -6.12244898 + 6.12244898 = 0.00000000 0.00000000 + x = -101.200622585 + 6.12244898 x = -101.200622585 + 6.12244898 Combine like terms: -101.200622585 + 6.12244898 = -95.078173605 x = -95.078173605 Simplifying x = -95.078173605Solution
The solution to the problem is based on the solutions from the subproblems. x = {107.323071565, -95.078173605}
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