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Simplifying (0.36x2) + -9x + -7000 = 0 Reorder the terms: -7000 + -9x + (0.36x2) = 0 Solving -7000 + -9x + (0.36x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.36 the coefficient of the squared term: Divide each side by '0.36'. -19444.44444 + -25x + x2 = 0 Move the constant term to the right: Add '19444.44444' to each side of the equation. -19444.44444 + -25x + 19444.44444 + x2 = 0 + 19444.44444 Reorder the terms: -19444.44444 + 19444.44444 + -25x + x2 = 0 + 19444.44444 Combine like terms: -19444.44444 + 19444.44444 = 0.00000 0.00000 + -25x + x2 = 0 + 19444.44444 -25x + x2 = 0 + 19444.44444 Combine like terms: 0 + 19444.44444 = 19444.44444 -25x + x2 = 19444.44444 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = 19444.44444 + 156.25 Reorder the terms: 156.25 + -25x + x2 = 19444.44444 + 156.25 Combine like terms: 19444.44444 + 156.25 = 19600.69444 156.25 + -25x + x2 = 19600.69444 Factor a perfect square on the left side: ((x) + -12.5)((x) + -12.5) = 19600.69444 Calculate the square root of the right side: 140.002480121 Break this problem into two subproblems by setting ((x) + -12.5) equal to 140.002480121 and -140.002480121.Subproblem 1
(x) + -12.5 = 140.002480121 Simplifying (x) + -12.5 = 140.002480121 x + -12.5 = 140.002480121 Reorder the terms: -12.5 + x = 140.002480121 Solving -12.5 + x = 140.002480121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 140.002480121 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 140.002480121 + 12.5 x = 140.002480121 + 12.5 Combine like terms: 140.002480121 + 12.5 = 152.502480121 x = 152.502480121 Simplifying x = 152.502480121Subproblem 2
(x) + -12.5 = -140.002480121 Simplifying (x) + -12.5 = -140.002480121 x + -12.5 = -140.002480121 Reorder the terms: -12.5 + x = -140.002480121 Solving -12.5 + x = -140.002480121 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -140.002480121 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -140.002480121 + 12.5 x = -140.002480121 + 12.5 Combine like terms: -140.002480121 + 12.5 = -127.502480121 x = -127.502480121 Simplifying x = -127.502480121Solution
The solution to the problem is based on the solutions from the subproblems. x = {152.502480121, -127.502480121}
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