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Simplifying 50x + 120x(92 + -1x) = 8380 50x + (92 * 120x + -1x * 120x) = 8380 50x + (11040x + -120x2) = 8380 Combine like terms: 50x + 11040x = 11090x 11090x + -120x2 = 8380 Solving 11090x + -120x2 = 8380 Solving for variable 'x'. Reorder the terms: -8380 + 11090x + -120x2 = 8380 + -8380 Combine like terms: 8380 + -8380 = 0 -8380 + 11090x + -120x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-838 + 1109x + -12x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-838 + 1109x + -12x2)' equal to zero and attempt to solve: Simplifying -838 + 1109x + -12x2 = 0 Solving -838 + 1109x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 69.83333333 + -92.41666667x + x2 = 0 Move the constant term to the right: Add '-69.83333333' to each side of the equation. 69.83333333 + -92.41666667x + -69.83333333 + x2 = 0 + -69.83333333 Reorder the terms: 69.83333333 + -69.83333333 + -92.41666667x + x2 = 0 + -69.83333333 Combine like terms: 69.83333333 + -69.83333333 = 0.00000000 0.00000000 + -92.41666667x + x2 = 0 + -69.83333333 -92.41666667x + x2 = 0 + -69.83333333 Combine like terms: 0 + -69.83333333 = -69.83333333 -92.41666667x + x2 = -69.83333333 The x term is -92.41666667x. Take half its coefficient (-46.20833334). Square it (2135.210070) and add it to both sides. Add '2135.210070' to each side of the equation. -92.41666667x + 2135.210070 + x2 = -69.83333333 + 2135.210070 Reorder the terms: 2135.210070 + -92.41666667x + x2 = -69.83333333 + 2135.210070 Combine like terms: -69.83333333 + 2135.210070 = 2065.37673667 2135.210070 + -92.41666667x + x2 = 2065.37673667 Factor a perfect square on the left side: (x + -46.20833334)(x + -46.20833334) = 2065.37673667 Calculate the square root of the right side: 45.446416104 Break this problem into two subproblems by setting (x + -46.20833334) equal to 45.446416104 and -45.446416104.Subproblem 1
x + -46.20833334 = 45.446416104 Simplifying x + -46.20833334 = 45.446416104 Reorder the terms: -46.20833334 + x = 45.446416104 Solving -46.20833334 + x = 45.446416104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.20833334' to each side of the equation. -46.20833334 + 46.20833334 + x = 45.446416104 + 46.20833334 Combine like terms: -46.20833334 + 46.20833334 = 0.00000000 0.00000000 + x = 45.446416104 + 46.20833334 x = 45.446416104 + 46.20833334 Combine like terms: 45.446416104 + 46.20833334 = 91.654749444 x = 91.654749444 Simplifying x = 91.654749444Subproblem 2
x + -46.20833334 = -45.446416104 Simplifying x + -46.20833334 = -45.446416104 Reorder the terms: -46.20833334 + x = -45.446416104 Solving -46.20833334 + x = -45.446416104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '46.20833334' to each side of the equation. -46.20833334 + 46.20833334 + x = -45.446416104 + 46.20833334 Combine like terms: -46.20833334 + 46.20833334 = 0.00000000 0.00000000 + x = -45.446416104 + 46.20833334 x = -45.446416104 + 46.20833334 Combine like terms: -45.446416104 + 46.20833334 = 0.761917236 x = 0.761917236 Simplifying x = 0.761917236Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.654749444, 0.761917236}Solution
x = {91.654749444, 0.761917236}
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