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Simplifying 0 = 3x2 + -26x + 30 Reorder the terms: 0 = 30 + -26x + 3x2 Solving 0 = 30 + -26x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -30 = -30 -30 + 26x + -3x2 = 30 + -26x + 3x2 + -30 + 26x + -3x2 Reorder the terms: -30 + 26x + -3x2 = 30 + -30 + -26x + 26x + 3x2 + -3x2 Combine like terms: 30 + -30 = 0 -30 + 26x + -3x2 = 0 + -26x + 26x + 3x2 + -3x2 -30 + 26x + -3x2 = -26x + 26x + 3x2 + -3x2 Combine like terms: -26x + 26x = 0 -30 + 26x + -3x2 = 0 + 3x2 + -3x2 -30 + 26x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -30 + 26x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 10 + -8.666666667x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8.666666667x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -8.666666667x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8.666666667x + x2 = 0 + -10 -8.666666667x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8.666666667x + x2 = -10 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 = -10 + 18.77777778 Reorder the terms: 18.77777778 + -8.666666667x + x2 = -10 + 18.77777778 Combine like terms: -10 + 18.77777778 = 8.77777778 18.77777778 + -8.666666667x + x2 = 8.77777778 Factor a perfect square on the left side: (x + -4.333333334)(x + -4.333333334) = 8.77777778 Calculate the square root of the right side: 2.962731473 Break this problem into two subproblems by setting (x + -4.333333334) equal to 2.962731473 and -2.962731473.Subproblem 1
x + -4.333333334 = 2.962731473 Simplifying x + -4.333333334 = 2.962731473 Reorder the terms: -4.333333334 + x = 2.962731473 Solving -4.333333334 + x = 2.962731473 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 = 2.962731473 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = 2.962731473 + 4.333333334 x = 2.962731473 + 4.333333334 Combine like terms: 2.962731473 + 4.333333334 = 7.296064807 x = 7.296064807 Simplifying x = 7.296064807Subproblem 2
x + -4.333333334 = -2.962731473 Simplifying x + -4.333333334 = -2.962731473 Reorder the terms: -4.333333334 + x = -2.962731473 Solving -4.333333334 + x = -2.962731473 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 = -2.962731473 + 4.333333334 Combine like terms: -4.333333334 + 4.333333334 = 0.000000000 0.000000000 + x = -2.962731473 + 4.333333334 x = -2.962731473 + 4.333333334 Combine like terms: -2.962731473 + 4.333333334 = 1.370601861 x = 1.370601861 Simplifying x = 1.370601861Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.296064807, 1.370601861}
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