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Simplifying 36x2 + -258x + 126 = 0 Reorder the terms: 126 + -258x + 36x2 = 0 Solving 126 + -258x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(21 + -43x + 6x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(21 + -43x + 6x2)' equal to zero and attempt to solve: Simplifying 21 + -43x + 6x2 = 0 Solving 21 + -43x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 3.5 + -7.166666667x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -7.166666667x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -7.166666667x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -7.166666667x + x2 = 0 + -3.5 -7.166666667x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -7.166666667x + x2 = -3.5 The x term is -7.166666667x. Take half its coefficient (-3.583333334). Square it (12.84027778) and add it to both sides. Add '12.84027778' to each side of the equation. -7.166666667x + 12.84027778 + x2 = -3.5 + 12.84027778 Reorder the terms: 12.84027778 + -7.166666667x + x2 = -3.5 + 12.84027778 Combine like terms: -3.5 + 12.84027778 = 9.34027778 12.84027778 + -7.166666667x + x2 = 9.34027778 Factor a perfect square on the left side: (x + -3.583333334)(x + -3.583333334) = 9.34027778 Calculate the square root of the right side: 3.056186804 Break this problem into two subproblems by setting (x + -3.583333334) equal to 3.056186804 and -3.056186804.Subproblem 1
x + -3.583333334 = 3.056186804 Simplifying x + -3.583333334 = 3.056186804 Reorder the terms: -3.583333334 + x = 3.056186804 Solving -3.583333334 + x = 3.056186804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = 3.056186804 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = 3.056186804 + 3.583333334 x = 3.056186804 + 3.583333334 Combine like terms: 3.056186804 + 3.583333334 = 6.639520138 x = 6.639520138 Simplifying x = 6.639520138Subproblem 2
x + -3.583333334 = -3.056186804 Simplifying x + -3.583333334 = -3.056186804 Reorder the terms: -3.583333334 + x = -3.056186804 Solving -3.583333334 + x = -3.056186804 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = -3.056186804 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = -3.056186804 + 3.583333334 x = -3.056186804 + 3.583333334 Combine like terms: -3.056186804 + 3.583333334 = 0.52714653 x = 0.52714653 Simplifying x = 0.52714653Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.639520138, 0.52714653}Solution
x = {6.639520138, 0.52714653}
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