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Simplifying 3x2 + -10x = 33 Reorder the terms: -10x + 3x2 = 33 Solving -10x + 3x2 = 33 Solving for variable 'x'. Reorder the terms: -33 + -10x + 3x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -33 + -10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -3.333333333x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -3.333333333x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -3.333333333x + x2 = 0 + 11 -3.333333333x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -3.333333333x + x2 = 11 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 11 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 11 + 2.777777779 Combine like terms: 11 + 2.777777779 = 13.777777779 2.777777779 + -3.333333333x + x2 = 13.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 13.777777779 Calculate the square root of the right side: 3.711842909 Break this problem into two subproblems by setting (x + -1.666666667) equal to 3.711842909 and -3.711842909.Subproblem 1
x + -1.666666667 = 3.711842909 Simplifying x + -1.666666667 = 3.711842909 Reorder the terms: -1.666666667 + x = 3.711842909 Solving -1.666666667 + x = 3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 3.711842909 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 3.711842909 + 1.666666667 x = 3.711842909 + 1.666666667 Combine like terms: 3.711842909 + 1.666666667 = 5.378509576 x = 5.378509576 Simplifying x = 5.378509576Subproblem 2
x + -1.666666667 = -3.711842909 Simplifying x + -1.666666667 = -3.711842909 Reorder the terms: -1.666666667 + x = -3.711842909 Solving -1.666666667 + x = -3.711842909 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -3.711842909 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -3.711842909 + 1.666666667 x = -3.711842909 + 1.666666667 Combine like terms: -3.711842909 + 1.666666667 = -2.045176242 x = -2.045176242 Simplifying x = -2.045176242Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.378509576, -2.045176242}
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