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Simplifying 150x + -1(3100 + 5x + 0.1x2) = 0 150x + (3100 * -1 + 5x * -1 + 0.1x2 * -1) = 0 150x + (-3100 + -5x + -0.1x2) = 0 Reorder the terms: -3100 + 150x + -5x + -0.1x2 = 0 Combine like terms: 150x + -5x = 145x -3100 + 145x + -0.1x2 = 0 Solving -3100 + 145x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 31000 + -1450x + x2 = 0 Move the constant term to the right: Add '-31000' to each side of the equation. 31000 + -1450x + -31000 + x2 = 0 + -31000 Reorder the terms: 31000 + -31000 + -1450x + x2 = 0 + -31000 Combine like terms: 31000 + -31000 = 0 0 + -1450x + x2 = 0 + -31000 -1450x + x2 = 0 + -31000 Combine like terms: 0 + -31000 = -31000 -1450x + x2 = -31000 The x term is -1450x. Take half its coefficient (-725). Square it (525625) and add it to both sides. Add '525625' to each side of the equation. -1450x + 525625 + x2 = -31000 + 525625 Reorder the terms: 525625 + -1450x + x2 = -31000 + 525625 Combine like terms: -31000 + 525625 = 494625 525625 + -1450x + x2 = 494625 Factor a perfect square on the left side: (x + -725)(x + -725) = 494625 Calculate the square root of the right side: 703.295812585 Break this problem into two subproblems by setting (x + -725) equal to 703.295812585 and -703.295812585.Subproblem 1
x + -725 = 703.295812585 Simplifying x + -725 = 703.295812585 Reorder the terms: -725 + x = 703.295812585 Solving -725 + x = 703.295812585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '725' to each side of the equation. -725 + 725 + x = 703.295812585 + 725 Combine like terms: -725 + 725 = 0 0 + x = 703.295812585 + 725 x = 703.295812585 + 725 Combine like terms: 703.295812585 + 725 = 1428.295812585 x = 1428.295812585 Simplifying x = 1428.295812585Subproblem 2
x + -725 = -703.295812585 Simplifying x + -725 = -703.295812585 Reorder the terms: -725 + x = -703.295812585 Solving -725 + x = -703.295812585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '725' to each side of the equation. -725 + 725 + x = -703.295812585 + 725 Combine like terms: -725 + 725 = 0 0 + x = -703.295812585 + 725 x = -703.295812585 + 725 Combine like terms: -703.295812585 + 725 = 21.704187415 x = 21.704187415 Simplifying x = 21.704187415Solution
The solution to the problem is based on the solutions from the subproblems. x = {1428.295812585, 21.704187415}
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