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Simplifying 2x + x(x + -50) = 15000 Reorder the terms: 2x + x(-50 + x) = 15000 2x + (-50 * x + x * x) = 15000 2x + (-50x + x2) = 15000 Combine like terms: 2x + -50x = -48x -48x + x2 = 15000 Solving -48x + x2 = 15000 Solving for variable 'x'. Reorder the terms: -15000 + -48x + x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 -15000 + -48x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15000' to each side of the equation. -15000 + -48x + 15000 + x2 = 0 + 15000 Reorder the terms: -15000 + 15000 + -48x + x2 = 0 + 15000 Combine like terms: -15000 + 15000 = 0 0 + -48x + x2 = 0 + 15000 -48x + x2 = 0 + 15000 Combine like terms: 0 + 15000 = 15000 -48x + x2 = 15000 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = 15000 + 576 Reorder the terms: 576 + -48x + x2 = 15000 + 576 Combine like terms: 15000 + 576 = 15576 576 + -48x + x2 = 15576 Factor a perfect square on the left side: (x + -24)(x + -24) = 15576 Calculate the square root of the right side: 124.803846095 Break this problem into two subproblems by setting (x + -24) equal to 124.803846095 and -124.803846095.Subproblem 1
x + -24 = 124.803846095 Simplifying x + -24 = 124.803846095 Reorder the terms: -24 + x = 124.803846095 Solving -24 + x = 124.803846095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 124.803846095 + 24 Combine like terms: -24 + 24 = 0 0 + x = 124.803846095 + 24 x = 124.803846095 + 24 Combine like terms: 124.803846095 + 24 = 148.803846095 x = 148.803846095 Simplifying x = 148.803846095Subproblem 2
x + -24 = -124.803846095 Simplifying x + -24 = -124.803846095 Reorder the terms: -24 + x = -124.803846095 Solving -24 + x = -124.803846095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -124.803846095 + 24 Combine like terms: -24 + 24 = 0 0 + x = -124.803846095 + 24 x = -124.803846095 + 24 Combine like terms: -124.803846095 + 24 = -100.803846095 x = -100.803846095 Simplifying x = -100.803846095Solution
The solution to the problem is based on the solutions from the subproblems. x = {148.803846095, -100.803846095}
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