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Simplifying 12x2 + -400x + 240 = 0 Reorder the terms: 240 + -400x + 12x2 = 0 Solving 240 + -400x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(60 + -100x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(60 + -100x + 3x2)' equal to zero and attempt to solve: Simplifying 60 + -100x + 3x2 = 0 Solving 60 + -100x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 20 + -33.33333333x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -33.33333333x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -33.33333333x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -33.33333333x + x2 = 0 + -20 -33.33333333x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -33.33333333x + x2 = -20 The x term is -33.33333333x. Take half its coefficient (-16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. -33.33333333x + 277.7777779 + x2 = -20 + 277.7777779 Reorder the terms: 277.7777779 + -33.33333333x + x2 = -20 + 277.7777779 Combine like terms: -20 + 277.7777779 = 257.7777779 277.7777779 + -33.33333333x + x2 = 257.7777779 Factor a perfect square on the left side: (x + -16.66666667)(x + -16.66666667) = 257.7777779 Calculate the square root of the right side: 16.055459442 Break this problem into two subproblems by setting (x + -16.66666667) equal to 16.055459442 and -16.055459442.Subproblem 1
x + -16.66666667 = 16.055459442 Simplifying x + -16.66666667 = 16.055459442 Reorder the terms: -16.66666667 + x = 16.055459442 Solving -16.66666667 + x = 16.055459442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = 16.055459442 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = 16.055459442 + 16.66666667 x = 16.055459442 + 16.66666667 Combine like terms: 16.055459442 + 16.66666667 = 32.722126112 x = 32.722126112 Simplifying x = 32.722126112Subproblem 2
x + -16.66666667 = -16.055459442 Simplifying x + -16.66666667 = -16.055459442 Reorder the terms: -16.66666667 + x = -16.055459442 Solving -16.66666667 + x = -16.055459442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = -16.055459442 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = -16.055459442 + 16.66666667 x = -16.055459442 + 16.66666667 Combine like terms: -16.055459442 + 16.66666667 = 0.611207228 x = 0.611207228 Simplifying x = 0.611207228Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.722126112, 0.611207228}Solution
x = {32.722126112, 0.611207228}
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