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Simplifying 12x2 + -80x + 96 = 0 Reorder the terms: 96 + -80x + 12x2 = 0 Solving 96 + -80x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(24 + -20x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -20x + 3x2)' equal to zero and attempt to solve: Simplifying 24 + -20x + 3x2 = 0 Solving 24 + -20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6.666666667x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -6.666666667x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6.666666667x + x2 = 0 + -8 -6.666666667x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6.666666667x + x2 = -8 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = -8 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -8 + 11.11111112 Combine like terms: -8 + 11.11111112 = 3.11111112 11.11111112 + -6.666666667x + x2 = 3.11111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 3.11111112 Calculate the square root of the right side: 1.76383421 Break this problem into two subproblems by setting (x + -3.333333334) equal to 1.76383421 and -1.76383421.Subproblem 1
x + -3.333333334 = 1.76383421 Simplifying x + -3.333333334 = 1.76383421 Reorder the terms: -3.333333334 + x = 1.76383421 Solving -3.333333334 + x = 1.76383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 1.76383421 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 1.76383421 + 3.333333334 x = 1.76383421 + 3.333333334 Combine like terms: 1.76383421 + 3.333333334 = 5.097167544 x = 5.097167544 Simplifying x = 5.097167544Subproblem 2
x + -3.333333334 = -1.76383421 Simplifying x + -3.333333334 = -1.76383421 Reorder the terms: -3.333333334 + x = -1.76383421 Solving -3.333333334 + x = -1.76383421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -1.76383421 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -1.76383421 + 3.333333334 x = -1.76383421 + 3.333333334 Combine like terms: -1.76383421 + 3.333333334 = 1.569499124 x = 1.569499124 Simplifying x = 1.569499124Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.097167544, 1.569499124}Solution
x = {5.097167544, 1.569499124}
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