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Simplifying 9x2 + -60x + 88 = 0 Reorder the terms: 88 + -60x + 9x2 = 0 Solving 88 + -60x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 9.777777778 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-9.777777778' to each side of the equation. 9.777777778 + -6.666666667x + -9.777777778 + x2 = 0 + -9.777777778 Reorder the terms: 9.777777778 + -9.777777778 + -6.666666667x + x2 = 0 + -9.777777778 Combine like terms: 9.777777778 + -9.777777778 = 0.000000000 0.000000000 + -6.666666667x + x2 = 0 + -9.777777778 -6.666666667x + x2 = 0 + -9.777777778 Combine like terms: 0 + -9.777777778 = -9.777777778 -6.666666667x + x2 = -9.777777778 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 = -9.777777778 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -9.777777778 + 11.11111112 Combine like terms: -9.777777778 + 11.11111112 = 1.333333342 11.11111112 + -6.666666667x + x2 = 1.333333342 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 1.333333342 Calculate the square root of the right side: 1.154700542 Break this problem into two subproblems by setting (x + -3.333333334) equal to 1.154700542 and -1.154700542.Subproblem 1
x + -3.333333334 = 1.154700542 Simplifying x + -3.333333334 = 1.154700542 Reorder the terms: -3.333333334 + x = 1.154700542 Solving -3.333333334 + x = 1.154700542 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 = 1.154700542 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 1.154700542 + 3.333333334 x = 1.154700542 + 3.333333334 Combine like terms: 1.154700542 + 3.333333334 = 4.488033876 x = 4.488033876 Simplifying x = 4.488033876Subproblem 2
x + -3.333333334 = -1.154700542 Simplifying x + -3.333333334 = -1.154700542 Reorder the terms: -3.333333334 + x = -1.154700542 Solving -3.333333334 + x = -1.154700542 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 = -1.154700542 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -1.154700542 + 3.333333334 x = -1.154700542 + 3.333333334 Combine like terms: -1.154700542 + 3.333333334 = 2.178632792 x = 2.178632792 Simplifying x = 2.178632792Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.488033876, 2.178632792}
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