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Simplifying 226.8 = (12 + -1x)(7 + -1x)(3) Reorder the terms for easier multiplication: 226.8 = 3(12 + -1x)(7 + -1x) Multiply (12 + -1x) * (7 + -1x) 226.8 = 3(12(7 + -1x) + -1x * (7 + -1x)) 226.8 = 3((7 * 12 + -1x * 12) + -1x * (7 + -1x)) 226.8 = 3((84 + -12x) + -1x * (7 + -1x)) 226.8 = 3(84 + -12x + (7 * -1x + -1x * -1x)) 226.8 = 3(84 + -12x + (-7x + 1x2)) Combine like terms: -12x + -7x = -19x 226.8 = 3(84 + -19x + 1x2) 226.8 = (84 * 3 + -19x * 3 + 1x2 * 3) 226.8 = (252 + -57x + 3x2) Solving 226.8 = 252 + -57x + 3x2 Solving for variable 'x'. Combine like terms: 226.8 + -252 = -25.2 -25.2 + 57x + -3x2 = 252 + -57x + 3x2 + -252 + 57x + -3x2 Reorder the terms: -25.2 + 57x + -3x2 = 252 + -252 + -57x + 57x + 3x2 + -3x2 Combine like terms: 252 + -252 = 0 -25.2 + 57x + -3x2 = 0 + -57x + 57x + 3x2 + -3x2 -25.2 + 57x + -3x2 = -57x + 57x + 3x2 + -3x2 Combine like terms: -57x + 57x = 0 -25.2 + 57x + -3x2 = 0 + 3x2 + -3x2 -25.2 + 57x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -25.2 + 57x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 8.4 + -19x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + -19x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + -19x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + -19x + x2 = 0 + -8.4 -19x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 -19x + x2 = -8.4 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 = -8.4 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -8.4 + 90.25 Combine like terms: -8.4 + 90.25 = 81.85 90.25 + -19x + x2 = 81.85 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 81.85 Calculate the square root of the right side: 9.047098983 Break this problem into two subproblems by setting (x + -9.5) equal to 9.047098983 and -9.047098983.Subproblem 1
x + -9.5 = 9.047098983 Simplifying x + -9.5 = 9.047098983 Reorder the terms: -9.5 + x = 9.047098983 Solving -9.5 + x = 9.047098983 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 = 9.047098983 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 9.047098983 + 9.5 x = 9.047098983 + 9.5 Combine like terms: 9.047098983 + 9.5 = 18.547098983 x = 18.547098983 Simplifying x = 18.547098983Subproblem 2
x + -9.5 = -9.047098983 Simplifying x + -9.5 = -9.047098983 Reorder the terms: -9.5 + x = -9.047098983 Solving -9.5 + x = -9.047098983 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 = -9.047098983 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -9.047098983 + 9.5 x = -9.047098983 + 9.5 Combine like terms: -9.047098983 + 9.5 = 0.452901017 x = 0.452901017 Simplifying x = 0.452901017Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.547098983, 0.452901017}
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