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Simplifying 12x2 + -40x + 24 = 0 Reorder the terms: 24 + -40x + 12x2 = 0 Solving 24 + -40x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -10x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -10x + 3x2)' equal to zero and attempt to solve: Simplifying 6 + -10x + 3x2 = 0 Solving 6 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.333333333x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.333333333x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.333333333x + x2 = 0 + -2 -3.333333333x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.333333333x + x2 = -2 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -2 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -2 + 2.777777779 Combine like terms: -2 + 2.777777779 = 0.777777779 2.777777779 + -3.333333333x + x2 = 0.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 0.777777779 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + -1.666666667) equal to 0.881917104 and -0.881917104.Subproblem 1
x + -1.666666667 = 0.881917104 Simplifying x + -1.666666667 = 0.881917104 Reorder the terms: -1.666666667 + x = 0.881917104 Solving -1.666666667 + x = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 0.881917104 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 0.881917104 + 1.666666667 x = 0.881917104 + 1.666666667 Combine like terms: 0.881917104 + 1.666666667 = 2.548583771 x = 2.548583771 Simplifying x = 2.548583771Subproblem 2
x + -1.666666667 = -0.881917104 Simplifying x + -1.666666667 = -0.881917104 Reorder the terms: -1.666666667 + x = -0.881917104 Solving -1.666666667 + x = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -0.881917104 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -0.881917104 + 1.666666667 x = -0.881917104 + 1.666666667 Combine like terms: -0.881917104 + 1.666666667 = 0.784749563 x = 0.784749563 Simplifying x = 0.784749563Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.548583771, 0.784749563}Solution
x = {2.548583771, 0.784749563}
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