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Simplifying 0 = 3x2 + -16x + -9 Reorder the terms: 0 = -9 + -16x + 3x2 Solving 0 = -9 + -16x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + 16x + -3x2 = -9 + -16x + 3x2 + 9 + 16x + -3x2 Reorder the terms: 9 + 16x + -3x2 = -9 + 9 + -16x + 16x + 3x2 + -3x2 Combine like terms: -9 + 9 = 0 9 + 16x + -3x2 = 0 + -16x + 16x + 3x2 + -3x2 9 + 16x + -3x2 = -16x + 16x + 3x2 + -3x2 Combine like terms: -16x + 16x = 0 9 + 16x + -3x2 = 0 + 3x2 + -3x2 9 + 16x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 9 + 16x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -3 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.333333333x + x2 = 0 + 3 -5.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.333333333x + x2 = 3 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 = 3 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = 3 + 7.111111113 Combine like terms: 3 + 7.111111113 = 10.111111113 7.111111113 + -5.333333333x + x2 = 10.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 10.111111113 Calculate the square root of the right side: 3.179797338 Break this problem into two subproblems by setting (x + -2.666666667) equal to 3.179797338 and -3.179797338.Subproblem 1
x + -2.666666667 = 3.179797338 Simplifying x + -2.666666667 = 3.179797338 Reorder the terms: -2.666666667 + x = 3.179797338 Solving -2.666666667 + x = 3.179797338 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 = 3.179797338 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 3.179797338 + 2.666666667 x = 3.179797338 + 2.666666667 Combine like terms: 3.179797338 + 2.666666667 = 5.846464005 x = 5.846464005 Simplifying x = 5.846464005Subproblem 2
x + -2.666666667 = -3.179797338 Simplifying x + -2.666666667 = -3.179797338 Reorder the terms: -2.666666667 + x = -3.179797338 Solving -2.666666667 + x = -3.179797338 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 = -3.179797338 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -3.179797338 + 2.666666667 x = -3.179797338 + 2.666666667 Combine like terms: -3.179797338 + 2.666666667 = -0.513130671 x = -0.513130671 Simplifying x = -0.513130671Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.846464005, -0.513130671}
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