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Simplifying 12x2 + -440x + 240 = 0 Reorder the terms: 240 + -440x + 12x2 = 0 Solving 240 + -440x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(60 + -110x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(60 + -110x + 3x2)' equal to zero and attempt to solve: Simplifying 60 + -110x + 3x2 = 0 Solving 60 + -110x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 20 + -36.66666667x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -36.66666667x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -36.66666667x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -36.66666667x + x2 = 0 + -20 -36.66666667x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -36.66666667x + x2 = -20 The x term is -36.66666667x. Take half its coefficient (-18.33333334). Square it (336.1111114) and add it to both sides. Add '336.1111114' to each side of the equation. -36.66666667x + 336.1111114 + x2 = -20 + 336.1111114 Reorder the terms: 336.1111114 + -36.66666667x + x2 = -20 + 336.1111114 Combine like terms: -20 + 336.1111114 = 316.1111114 336.1111114 + -36.66666667x + x2 = 316.1111114 Factor a perfect square on the left side: (x + -18.33333334)(x + -18.33333334) = 316.1111114 Calculate the square root of the right side: 17.779513812 Break this problem into two subproblems by setting (x + -18.33333334) equal to 17.779513812 and -17.779513812.Subproblem 1
x + -18.33333334 = 17.779513812 Simplifying x + -18.33333334 = 17.779513812 Reorder the terms: -18.33333334 + x = 17.779513812 Solving -18.33333334 + x = 17.779513812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.33333334' to each side of the equation. -18.33333334 + 18.33333334 + x = 17.779513812 + 18.33333334 Combine like terms: -18.33333334 + 18.33333334 = 0.00000000 0.00000000 + x = 17.779513812 + 18.33333334 x = 17.779513812 + 18.33333334 Combine like terms: 17.779513812 + 18.33333334 = 36.112847152 x = 36.112847152 Simplifying x = 36.112847152Subproblem 2
x + -18.33333334 = -17.779513812 Simplifying x + -18.33333334 = -17.779513812 Reorder the terms: -18.33333334 + x = -17.779513812 Solving -18.33333334 + x = -17.779513812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.33333334' to each side of the equation. -18.33333334 + 18.33333334 + x = -17.779513812 + 18.33333334 Combine like terms: -18.33333334 + 18.33333334 = 0.00000000 0.00000000 + x = -17.779513812 + 18.33333334 x = -17.779513812 + 18.33333334 Combine like terms: -17.779513812 + 18.33333334 = 0.553819528 x = 0.553819528 Simplifying x = 0.553819528Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.112847152, 0.553819528}Solution
x = {36.112847152, 0.553819528}
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