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Simplifying 3x2 + -11x + -10 = 22 Reorder the terms: -10 + -11x + 3x2 = 22 Solving -10 + -11x + 3x2 = 22 Solving for variable 'x'. Reorder the terms: -10 + -22 + -11x + 3x2 = 22 + -22 Combine like terms: -10 + -22 = -32 -32 + -11x + 3x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -32 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10.66666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '10.66666667' to each side of the equation. -10.66666667 + -3.666666667x + 10.66666667 + x2 = 0 + 10.66666667 Reorder the terms: -10.66666667 + 10.66666667 + -3.666666667x + x2 = 0 + 10.66666667 Combine like terms: -10.66666667 + 10.66666667 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 10.66666667 -3.666666667x + x2 = 0 + 10.66666667 Combine like terms: 0 + 10.66666667 = 10.66666667 -3.666666667x + x2 = 10.66666667 The x term is -3.666666667x. Take half its coefficient (-1.833333334). Square it (3.361111114) and add it to both sides. Add '3.361111114' to each side of the equation. -3.666666667x + 3.361111114 + x2 = 10.66666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 10.66666667 + 3.361111114 Combine like terms: 10.66666667 + 3.361111114 = 14.027777784 3.361111114 + -3.666666667x + x2 = 14.027777784 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 14.027777784 Calculate the square root of the right side: 3.74536751 Break this problem into two subproblems by setting (x + -1.833333334) equal to 3.74536751 and -3.74536751.Subproblem 1
x + -1.833333334 = 3.74536751 Simplifying x + -1.833333334 = 3.74536751 Reorder the terms: -1.833333334 + x = 3.74536751 Solving -1.833333334 + x = 3.74536751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 3.74536751 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 3.74536751 + 1.833333334 x = 3.74536751 + 1.833333334 Combine like terms: 3.74536751 + 1.833333334 = 5.578700844 x = 5.578700844 Simplifying x = 5.578700844Subproblem 2
x + -1.833333334 = -3.74536751 Simplifying x + -1.833333334 = -3.74536751 Reorder the terms: -1.833333334 + x = -3.74536751 Solving -1.833333334 + x = -3.74536751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -3.74536751 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -3.74536751 + 1.833333334 x = -3.74536751 + 1.833333334 Combine like terms: -3.74536751 + 1.833333334 = -1.912034176 x = -1.912034176 Simplifying x = -1.912034176Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.578700844, -1.912034176}
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