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Simplifying (13 + -1x)(6 + -1x)(4) = 280.8 Reorder the terms for easier multiplication: 4(13 + -1x)(6 + -1x) = 280.8 Multiply (13 + -1x) * (6 + -1x) 4(13(6 + -1x) + -1x * (6 + -1x)) = 280.8 4((6 * 13 + -1x * 13) + -1x * (6 + -1x)) = 280.8 4((78 + -13x) + -1x * (6 + -1x)) = 280.8 4(78 + -13x + (6 * -1x + -1x * -1x)) = 280.8 4(78 + -13x + (-6x + 1x2)) = 280.8 Combine like terms: -13x + -6x = -19x 4(78 + -19x + 1x2) = 280.8 (78 * 4 + -19x * 4 + 1x2 * 4) = 280.8 (312 + -76x + 4x2) = 280.8 Solving 312 + -76x + 4x2 = 280.8 Solving for variable 'x'. Reorder the terms: 312 + -280.8 + -76x + 4x2 = 280.8 + -280.8 Combine like terms: 312 + -280.8 = 31.2 31.2 + -76x + 4x2 = 280.8 + -280.8 Combine like terms: 280.8 + -280.8 = 0.0 31.2 + -76x + 4x2 = 0.0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.8 + -19x + x2 = 0.0 Move the constant term to the right: Add '-7.8' to each side of the equation. 7.8 + -19x + -7.8 + x2 = 0.0 + -7.8 Reorder the terms: 7.8 + -7.8 + -19x + x2 = 0.0 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + -19x + x2 = 0.0 + -7.8 -19x + x2 = 0.0 + -7.8 Combine like terms: 0.0 + -7.8 = -7.8 -19x + x2 = -7.8 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = -7.8 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -7.8 + 90.25 Combine like terms: -7.8 + 90.25 = 82.45 90.25 + -19x + x2 = 82.45 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 82.45 Calculate the square root of the right side: 9.080198236 Break this problem into two subproblems by setting (x + -9.5) equal to 9.080198236 and -9.080198236.Subproblem 1
x + -9.5 = 9.080198236 Simplifying x + -9.5 = 9.080198236 Reorder the terms: -9.5 + x = 9.080198236 Solving -9.5 + x = 9.080198236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 9.080198236 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.080198236 + 9.5 x = 9.080198236 + 9.5 Combine like terms: 9.080198236 + 9.5 = 18.580198236 x = 18.580198236 Simplifying x = 18.580198236Subproblem 2
x + -9.5 = -9.080198236 Simplifying x + -9.5 = -9.080198236 Reorder the terms: -9.5 + x = -9.080198236 Solving -9.5 + x = -9.080198236 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -9.080198236 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.080198236 + 9.5 x = -9.080198236 + 9.5 Combine like terms: -9.080198236 + 9.5 = 0.419801764 x = 0.419801764 Simplifying x = 0.419801764Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.580198236, 0.419801764}
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