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Simplifying 3x2 + -16x + 3 = 0 Reorder the terms: 3 + -16x + 3x2 = 0 Solving 3 + -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'. 1 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -5.333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -5.333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5.333333333x + x2 = 0 + -1 -5.333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5.333333333x + x2 = -1 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 = -1 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -1 + 7.111111113 Combine like terms: -1 + 7.111111113 = 6.111111113 7.111111113 + -5.333333333x + x2 = 6.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 6.111111113 Calculate the square root of the right side: 2.472066163 Break this problem into two subproblems by setting (x + -2.666666667) equal to 2.472066163 and -2.472066163.Subproblem 1
x + -2.666666667 = 2.472066163 Simplifying x + -2.666666667 = 2.472066163 Reorder the terms: -2.666666667 + x = 2.472066163 Solving -2.666666667 + x = 2.472066163 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 = 2.472066163 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 2.472066163 + 2.666666667 x = 2.472066163 + 2.666666667 Combine like terms: 2.472066163 + 2.666666667 = 5.13873283 x = 5.13873283 Simplifying x = 5.13873283Subproblem 2
x + -2.666666667 = -2.472066163 Simplifying x + -2.666666667 = -2.472066163 Reorder the terms: -2.666666667 + x = -2.472066163 Solving -2.666666667 + x = -2.472066163 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 = -2.472066163 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -2.472066163 + 2.666666667 x = -2.472066163 + 2.666666667 Combine like terms: -2.472066163 + 2.666666667 = 0.194600504 x = 0.194600504 Simplifying x = 0.194600504Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.13873283, 0.194600504}
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