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Simplifying 3x2 + 16x + -6 = 0 Reorder the terms: -6 + 16x + 3x2 = 0 Solving -6 + 16x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 5.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 5.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5.333333333x + x2 = 0 + 2 5.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 5.333333333x + x2 = 2 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 2 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 2 + 7.111111113 Combine like terms: 2 + 7.111111113 = 9.111111113 7.111111113 + 5.333333333x + x2 = 9.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 9.111111113 Calculate the square root of the right side: 3.018461713 Break this problem into two subproblems by setting (x + 2.666666667) equal to 3.018461713 and -3.018461713.Subproblem 1
x + 2.666666667 = 3.018461713 Simplifying x + 2.666666667 = 3.018461713 Reorder the terms: 2.666666667 + x = 3.018461713 Solving 2.666666667 + x = 3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 3.018461713 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 3.018461713 + -2.666666667 x = 3.018461713 + -2.666666667 Combine like terms: 3.018461713 + -2.666666667 = 0.351795046 x = 0.351795046 Simplifying x = 0.351795046Subproblem 2
x + 2.666666667 = -3.018461713 Simplifying x + 2.666666667 = -3.018461713 Reorder the terms: 2.666666667 + x = -3.018461713 Solving 2.666666667 + x = -3.018461713 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -3.018461713 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -3.018461713 + -2.666666667 x = -3.018461713 + -2.666666667 Combine like terms: -3.018461713 + -2.666666667 = -5.68512838 x = -5.68512838 Simplifying x = -5.68512838Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.351795046, -5.68512838}
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