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Simplifying 0 = 9x2 + -60x + 50 Reorder the terms: 0 = 50 + -60x + 9x2 Solving 0 = 50 + -60x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + 60x + -9x2 = 50 + -60x + 9x2 + -50 + 60x + -9x2 Reorder the terms: -50 + 60x + -9x2 = 50 + -50 + -60x + 60x + 9x2 + -9x2 Combine like terms: 50 + -50 = 0 -50 + 60x + -9x2 = 0 + -60x + 60x + 9x2 + -9x2 -50 + 60x + -9x2 = -60x + 60x + 9x2 + -9x2 Combine like terms: -60x + 60x = 0 -50 + 60x + -9x2 = 0 + 9x2 + -9x2 -50 + 60x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -50 + 60x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 5.555555556 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-5.555555556' to each side of the equation. 5.555555556 + -6.666666667x + -5.555555556 + x2 = 0 + -5.555555556 Reorder the terms: 5.555555556 + -5.555555556 + -6.666666667x + x2 = 0 + -5.555555556 Combine like terms: 5.555555556 + -5.555555556 = 0.000000000 0.000000000 + -6.666666667x + x2 = 0 + -5.555555556 -6.666666667x + x2 = 0 + -5.555555556 Combine like terms: 0 + -5.555555556 = -5.555555556 -6.666666667x + x2 = -5.555555556 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 = -5.555555556 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -5.555555556 + 11.11111112 Combine like terms: -5.555555556 + 11.11111112 = 5.555555564 11.11111112 + -6.666666667x + x2 = 5.555555564 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 5.555555564 Calculate the square root of the right side: 2.357022606 Break this problem into two subproblems by setting (x + -3.333333334) equal to 2.357022606 and -2.357022606.Subproblem 1
x + -3.333333334 = 2.357022606 Simplifying x + -3.333333334 = 2.357022606 Reorder the terms: -3.333333334 + x = 2.357022606 Solving -3.333333334 + x = 2.357022606 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 = 2.357022606 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 2.357022606 + 3.333333334 x = 2.357022606 + 3.333333334 Combine like terms: 2.357022606 + 3.333333334 = 5.69035594 x = 5.69035594 Simplifying x = 5.69035594Subproblem 2
x + -3.333333334 = -2.357022606 Simplifying x + -3.333333334 = -2.357022606 Reorder the terms: -3.333333334 + x = -2.357022606 Solving -3.333333334 + x = -2.357022606 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 = -2.357022606 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -2.357022606 + 3.333333334 x = -2.357022606 + 3.333333334 Combine like terms: -2.357022606 + 3.333333334 = 0.976310728 x = 0.976310728 Simplifying x = 0.976310728Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.69035594, 0.976310728}
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