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Simplifying 3x2 + -26x + 36 = 0 Reorder the terms: 36 + -26x + 3x2 = 0 Solving 36 + -26x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 12 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -8.666666667x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -8.666666667x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -8.666666667x + x2 = 0 + -12 -8.666666667x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -8.666666667x + x2 = -12 The x term is -8.666666667x. Take half its coefficient (-4.333333334). Square it (18.77777778) and add it to both sides. Add '18.77777778' to each side of the equation. -8.666666667x + 18.77777778 + x2 = -12 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = -12 + 18.77777778 Combine like terms: -12 + 18.77777778 = 6.77777778 18.77777778 + -8.666666667x + x2 = 6.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 6.77777778 Calculate the square root of the right side: 2.603416559 Break this problem into two subproblems by setting (x + -4.333333334) equal to 2.603416559 and -2.603416559.Subproblem 1
x + -4.333333334 = 2.603416559 Simplifying x + -4.333333334 = 2.603416559 Reorder the terms: -4.333333334 + x = 2.603416559 Solving -4.333333334 + x = 2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = 2.603416559 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 2.603416559 + 4.333333334 x = 2.603416559 + 4.333333334 Combine like terms: 2.603416559 + 4.333333334 = 6.936749893 x = 6.936749893 Simplifying x = 6.936749893Subproblem 2
x + -4.333333334 = -2.603416559 Simplifying x + -4.333333334 = -2.603416559 Reorder the terms: -4.333333334 + x = -2.603416559 Solving -4.333333334 + x = -2.603416559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.333333334' to each side of the equation. -4.333333334 + 4.333333334 + x = -2.603416559 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -2.603416559 + 4.333333334 x = -2.603416559 + 4.333333334 Combine like terms: -2.603416559 + 4.333333334 = 1.729916775 x = 1.729916775 Simplifying x = 1.729916775Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.936749893, 1.729916775}
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