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Simplifying 4x2 + 860x + 12000 + -118919 = 0 Reorder the terms: 12000 + -118919 + 860x + 4x2 = 0 Combine like terms: 12000 + -118919 = -106919 -106919 + 860x + 4x2 = 0 Solving -106919 + 860x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -26729.75 + 215x + x2 = 0 Move the constant term to the right: Add '26729.75' to each side of the equation. -26729.75 + 215x + 26729.75 + x2 = 0 + 26729.75 Reorder the terms: -26729.75 + 26729.75 + 215x + x2 = 0 + 26729.75 Combine like terms: -26729.75 + 26729.75 = 0.00 0.00 + 215x + x2 = 0 + 26729.75 215x + x2 = 0 + 26729.75 Combine like terms: 0 + 26729.75 = 26729.75 215x + x2 = 26729.75 The x term is 215x. Take half its coefficient (107.5). Square it (11556.25) and add it to both sides. Add '11556.25' to each side of the equation. 215x + 11556.25 + x2 = 26729.75 + 11556.25 Reorder the terms: 11556.25 + 215x + x2 = 26729.75 + 11556.25 Combine like terms: 26729.75 + 11556.25 = 38286 11556.25 + 215x + x2 = 38286 Factor a perfect square on the left side: (x + 107.5)(x + 107.5) = 38286 Calculate the square root of the right side: 195.668086309 Break this problem into two subproblems by setting (x + 107.5) equal to 195.668086309 and -195.668086309.Subproblem 1
x + 107.5 = 195.668086309 Simplifying x + 107.5 = 195.668086309 Reorder the terms: 107.5 + x = 195.668086309 Solving 107.5 + x = 195.668086309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-107.5' to each side of the equation. 107.5 + -107.5 + x = 195.668086309 + -107.5 Combine like terms: 107.5 + -107.5 = 0.0 0.0 + x = 195.668086309 + -107.5 x = 195.668086309 + -107.5 Combine like terms: 195.668086309 + -107.5 = 88.168086309 x = 88.168086309 Simplifying x = 88.168086309Subproblem 2
x + 107.5 = -195.668086309 Simplifying x + 107.5 = -195.668086309 Reorder the terms: 107.5 + x = -195.668086309 Solving 107.5 + x = -195.668086309 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-107.5' to each side of the equation. 107.5 + -107.5 + x = -195.668086309 + -107.5 Combine like terms: 107.5 + -107.5 = 0.0 0.0 + x = -195.668086309 + -107.5 x = -195.668086309 + -107.5 Combine like terms: -195.668086309 + -107.5 = -303.168086309 x = -303.168086309 Simplifying x = -303.168086309Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.168086309, -303.168086309}
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