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Simplifying 3x2 + -11x + 6 = 65 Reorder the terms: 6 + -11x + 3x2 = 65 Solving 6 + -11x + 3x2 = 65 Solving for variable 'x'. Reorder the terms: 6 + -65 + -11x + 3x2 = 65 + -65 Combine like terms: 6 + -65 = -59 -59 + -11x + 3x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -59 + -11x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -19.66666667 + -3.666666667x + x2 = 0 Move the constant term to the right: Add '19.66666667' to each side of the equation. -19.66666667 + -3.666666667x + 19.66666667 + x2 = 0 + 19.66666667 Reorder the terms: -19.66666667 + 19.66666667 + -3.666666667x + x2 = 0 + 19.66666667 Combine like terms: -19.66666667 + 19.66666667 = 0.00000000 0.00000000 + -3.666666667x + x2 = 0 + 19.66666667 -3.666666667x + x2 = 0 + 19.66666667 Combine like terms: 0 + 19.66666667 = 19.66666667 -3.666666667x + x2 = 19.66666667 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 = 19.66666667 + 3.361111114 Reorder the terms: 3.361111114 + -3.666666667x + x2 = 19.66666667 + 3.361111114 Combine like terms: 19.66666667 + 3.361111114 = 23.027777784 3.361111114 + -3.666666667x + x2 = 23.027777784 Factor a perfect square on the left side: (x + -1.833333334)(x + -1.833333334) = 23.027777784 Calculate the square root of the right side: 4.798726684 Break this problem into two subproblems by setting (x + -1.833333334) equal to 4.798726684 and -4.798726684.Subproblem 1
x + -1.833333334 = 4.798726684 Simplifying x + -1.833333334 = 4.798726684 Reorder the terms: -1.833333334 + x = 4.798726684 Solving -1.833333334 + x = 4.798726684 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 = 4.798726684 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 4.798726684 + 1.833333334 x = 4.798726684 + 1.833333334 Combine like terms: 4.798726684 + 1.833333334 = 6.632060018 x = 6.632060018 Simplifying x = 6.632060018Subproblem 2
x + -1.833333334 = -4.798726684 Simplifying x + -1.833333334 = -4.798726684 Reorder the terms: -1.833333334 + x = -4.798726684 Solving -1.833333334 + x = -4.798726684 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 = -4.798726684 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -4.798726684 + 1.833333334 x = -4.798726684 + 1.833333334 Combine like terms: -4.798726684 + 1.833333334 = -2.96539335 x = -2.96539335 Simplifying x = -2.96539335Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.632060018, -2.96539335}
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