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Simplifying 3x2 + -16x + 18 = 0 Reorder the terms: 18 + -16x + 3x2 = 0 Solving 18 + -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'. 6 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -5.333333333x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -5.333333333x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5.333333333x + x2 = 0 + -6 -5.333333333x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -5.333333333x + x2 = -6 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 = -6 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = -6 + 7.111111113 Combine like terms: -6 + 7.111111113 = 1.111111113 7.111111113 + -5.333333333x + x2 = 1.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 1.111111113 Calculate the square root of the right side: 1.054092554 Break this problem into two subproblems by setting (x + -2.666666667) equal to 1.054092554 and -1.054092554.Subproblem 1
x + -2.666666667 = 1.054092554 Simplifying x + -2.666666667 = 1.054092554 Reorder the terms: -2.666666667 + x = 1.054092554 Solving -2.666666667 + x = 1.054092554 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 = 1.054092554 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 1.054092554 + 2.666666667 x = 1.054092554 + 2.666666667 Combine like terms: 1.054092554 + 2.666666667 = 3.720759221 x = 3.720759221 Simplifying x = 3.720759221Subproblem 2
x + -2.666666667 = -1.054092554 Simplifying x + -2.666666667 = -1.054092554 Reorder the terms: -2.666666667 + x = -1.054092554 Solving -2.666666667 + x = -1.054092554 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 = -1.054092554 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -1.054092554 + 2.666666667 x = -1.054092554 + 2.666666667 Combine like terms: -1.054092554 + 2.666666667 = 1.612574113 x = 1.612574113 Simplifying x = 1.612574113Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.720759221, 1.612574113}
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