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Simplifying 180000 = x2 + 3x Reorder the terms: 180000 = 3x + x2 Solving 180000 = 3x + x2 Solving for variable 'x'. Reorder the terms: 180000 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 180000 + -3x + -1x2 = 0 + x2 + -1x2 180000 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180000 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180000 + 3x + x2 = 0 Move the constant term to the right: Add '180000' to each side of the equation. -180000 + 3x + 180000 + x2 = 0 + 180000 Reorder the terms: -180000 + 180000 + 3x + x2 = 0 + 180000 Combine like terms: -180000 + 180000 = 0 0 + 3x + x2 = 0 + 180000 3x + x2 = 0 + 180000 Combine like terms: 0 + 180000 = 180000 3x + x2 = 180000 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 180000 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 180000 + 2.25 Combine like terms: 180000 + 2.25 = 180002.25 2.25 + 3x + x2 = 180002.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 180002.25 Calculate the square root of the right side: 424.266720354 Break this problem into two subproblems by setting (x + 1.5) equal to 424.266720354 and -424.266720354.Subproblem 1
x + 1.5 = 424.266720354 Simplifying x + 1.5 = 424.266720354 Reorder the terms: 1.5 + x = 424.266720354 Solving 1.5 + x = 424.266720354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 424.266720354 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 424.266720354 + -1.5 x = 424.266720354 + -1.5 Combine like terms: 424.266720354 + -1.5 = 422.766720354 x = 422.766720354 Simplifying x = 422.766720354Subproblem 2
x + 1.5 = -424.266720354 Simplifying x + 1.5 = -424.266720354 Reorder the terms: 1.5 + x = -424.266720354 Solving 1.5 + x = -424.266720354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -424.266720354 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -424.266720354 + -1.5 x = -424.266720354 + -1.5 Combine like terms: -424.266720354 + -1.5 = -425.766720354 x = -425.766720354 Simplifying x = -425.766720354Solution
The solution to the problem is based on the solutions from the subproblems. x = {422.766720354, -425.766720354}
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