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Simplifying 267.9x + -3x2 = 15x + 3551.1 Reorder the terms: 267.9x + -3x2 = 3551.1 + 15x Solving 267.9x + -3x2 = 3551.1 + 15x Solving for variable 'x'. Reorder the terms: -3551.1 + 267.9x + -15x + -3x2 = 3551.1 + 15x + -3551.1 + -15x Combine like terms: 267.9x + -15x = 252.9x -3551.1 + 252.9x + -3x2 = 3551.1 + 15x + -3551.1 + -15x Reorder the terms: -3551.1 + 252.9x + -3x2 = 3551.1 + -3551.1 + 15x + -15x Combine like terms: 3551.1 + -3551.1 = 0.0 -3551.1 + 252.9x + -3x2 = 0.0 + 15x + -15x -3551.1 + 252.9x + -3x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -3551.1 + 252.9x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1183.7 + -84.3x + x2 = 0 Move the constant term to the right: Add '-1183.7' to each side of the equation. 1183.7 + -84.3x + -1183.7 + x2 = 0 + -1183.7 Reorder the terms: 1183.7 + -1183.7 + -84.3x + x2 = 0 + -1183.7 Combine like terms: 1183.7 + -1183.7 = 0.0 0.0 + -84.3x + x2 = 0 + -1183.7 -84.3x + x2 = 0 + -1183.7 Combine like terms: 0 + -1183.7 = -1183.7 -84.3x + x2 = -1183.7 The x term is -84.3x. Take half its coefficient (-42.15). Square it (1776.6225) and add it to both sides. Add '1776.6225' to each side of the equation. -84.3x + 1776.6225 + x2 = -1183.7 + 1776.6225 Reorder the terms: 1776.6225 + -84.3x + x2 = -1183.7 + 1776.6225 Combine like terms: -1183.7 + 1776.6225 = 592.9225 1776.6225 + -84.3x + x2 = 592.9225 Factor a perfect square on the left side: (x + -42.15)(x + -42.15) = 592.9225 Calculate the square root of the right side: 24.35 Break this problem into two subproblems by setting (x + -42.15) equal to 24.35 and -24.35.Subproblem 1
x + -42.15 = 24.35 Simplifying x + -42.15 = 24.35 Reorder the terms: -42.15 + x = 24.35 Solving -42.15 + x = 24.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.15' to each side of the equation. -42.15 + 42.15 + x = 24.35 + 42.15 Combine like terms: -42.15 + 42.15 = 0.00 0.00 + x = 24.35 + 42.15 x = 24.35 + 42.15 Combine like terms: 24.35 + 42.15 = 66.5 x = 66.5 Simplifying x = 66.5Subproblem 2
x + -42.15 = -24.35 Simplifying x + -42.15 = -24.35 Reorder the terms: -42.15 + x = -24.35 Solving -42.15 + x = -24.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.15' to each side of the equation. -42.15 + 42.15 + x = -24.35 + 42.15 Combine like terms: -42.15 + 42.15 = 0.00 0.00 + x = -24.35 + 42.15 x = -24.35 + 42.15 Combine like terms: -24.35 + 42.15 = 17.8 x = 17.8 Simplifying x = 17.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.5, 17.8}
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