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Simplifying 12(x2 + -40x + 30) = 0 Reorder the terms: 12(30 + -40x + x2) = 0 (30 * 12 + -40x * 12 + x2 * 12) = 0 (360 + -480x + 12x2) = 0 Solving 360 + -480x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(30 + -40x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(30 + -40x + x2)' equal to zero and attempt to solve: Simplifying 30 + -40x + x2 = 0 Solving 30 + -40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -40x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -40x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -40x + x2 = 0 + -30 -40x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -40x + x2 = -30 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -30 + 400 Reorder the terms: 400 + -40x + x2 = -30 + 400 Combine like terms: -30 + 400 = 370 400 + -40x + x2 = 370 Factor a perfect square on the left side: (x + -20)(x + -20) = 370 Calculate the square root of the right side: 19.235384062 Break this problem into two subproblems by setting (x + -20) equal to 19.235384062 and -19.235384062.Subproblem 1
x + -20 = 19.235384062 Simplifying x + -20 = 19.235384062 Reorder the terms: -20 + x = 19.235384062 Solving -20 + x = 19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.235384062 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.235384062 + 20 x = 19.235384062 + 20 Combine like terms: 19.235384062 + 20 = 39.235384062 x = 39.235384062 Simplifying x = 39.235384062Subproblem 2
x + -20 = -19.235384062 Simplifying x + -20 = -19.235384062 Reorder the terms: -20 + x = -19.235384062 Solving -20 + x = -19.235384062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.235384062 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.235384062 + 20 x = -19.235384062 + 20 Combine like terms: -19.235384062 + 20 = 0.764615938 x = 0.764615938 Simplifying x = 0.764615938Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.235384062, 0.764615938}Solution
x = {39.235384062, 0.764615938}
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