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Simplifying 12x2 + -176x + 480 = 0 Reorder the terms: 480 + -176x + 12x2 = 0 Solving 480 + -176x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(120 + -44x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(120 + -44x + 3x2)' equal to zero and attempt to solve: Simplifying 120 + -44x + 3x2 = 0 Solving 120 + -44x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 40 + -14.66666667x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -14.66666667x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -14.66666667x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -14.66666667x + x2 = 0 + -40 -14.66666667x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -14.66666667x + x2 = -40 The x term is -14.66666667x. Take half its coefficient (-7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. -14.66666667x + 53.77777780 + x2 = -40 + 53.77777780 Reorder the terms: 53.77777780 + -14.66666667x + x2 = -40 + 53.77777780 Combine like terms: -40 + 53.77777780 = 13.7777778 53.77777780 + -14.66666667x + x2 = 13.7777778 Factor a perfect square on the left side: (x + -7.333333335)(x + -7.333333335) = 13.7777778 Calculate the square root of the right side: 3.711842912 Break this problem into two subproblems by setting (x + -7.333333335) equal to 3.711842912 and -3.711842912.Subproblem 1
x + -7.333333335 = 3.711842912 Simplifying x + -7.333333335 = 3.711842912 Reorder the terms: -7.333333335 + x = 3.711842912 Solving -7.333333335 + x = 3.711842912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = 3.711842912 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = 3.711842912 + 7.333333335 x = 3.711842912 + 7.333333335 Combine like terms: 3.711842912 + 7.333333335 = 11.045176247 x = 11.045176247 Simplifying x = 11.045176247Subproblem 2
x + -7.333333335 = -3.711842912 Simplifying x + -7.333333335 = -3.711842912 Reorder the terms: -7.333333335 + x = -3.711842912 Solving -7.333333335 + x = -3.711842912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.333333335' to each side of the equation. -7.333333335 + 7.333333335 + x = -3.711842912 + 7.333333335 Combine like terms: -7.333333335 + 7.333333335 = 0.000000000 0.000000000 + x = -3.711842912 + 7.333333335 x = -3.711842912 + 7.333333335 Combine like terms: -3.711842912 + 7.333333335 = 3.621490423 x = 3.621490423 Simplifying x = 3.621490423Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.045176247, 3.621490423}Solution
x = {11.045176247, 3.621490423}
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