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Simplifying 12x2 + -92x + -68 = 0 Reorder the terms: -68 + -92x + 12x2 = 0 Solving -68 + -92x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-17 + -23x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-17 + -23x + 3x2)' equal to zero and attempt to solve: Simplifying -17 + -23x + 3x2 = 0 Solving -17 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.666666667 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '5.666666667' to each side of the equation. -5.666666667 + -7.666666667x + 5.666666667 + x2 = 0 + 5.666666667 Reorder the terms: -5.666666667 + 5.666666667 + -7.666666667x + x2 = 0 + 5.666666667 Combine like terms: -5.666666667 + 5.666666667 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + 5.666666667 -7.666666667x + x2 = 0 + 5.666666667 Combine like terms: 0 + 5.666666667 = 5.666666667 -7.666666667x + x2 = 5.666666667 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 5.666666667 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 5.666666667 + 14.69444445 Combine like terms: 5.666666667 + 14.69444445 = 20.361111117 14.69444445 + -7.666666667x + x2 = 20.361111117 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 20.361111117 Calculate the square root of the right side: 4.512328791 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.512328791 and -4.512328791.Subproblem 1
x + -3.833333334 = 4.512328791 Simplifying x + -3.833333334 = 4.512328791 Reorder the terms: -3.833333334 + x = 4.512328791 Solving -3.833333334 + x = 4.512328791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.512328791 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.512328791 + 3.833333334 x = 4.512328791 + 3.833333334 Combine like terms: 4.512328791 + 3.833333334 = 8.345662125 x = 8.345662125 Simplifying x = 8.345662125Subproblem 2
x + -3.833333334 = -4.512328791 Simplifying x + -3.833333334 = -4.512328791 Reorder the terms: -3.833333334 + x = -4.512328791 Solving -3.833333334 + x = -4.512328791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.512328791 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.512328791 + 3.833333334 x = -4.512328791 + 3.833333334 Combine like terms: -4.512328791 + 3.833333334 = -0.678995457 x = -0.678995457 Simplifying x = -0.678995457Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.345662125, -0.678995457}Solution
x = {8.345662125, -0.678995457}
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