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Simplifying 3x2 + 14x + 9 = -2x Reorder the terms: 9 + 14x + 3x2 = -2x Solving 9 + 14x + 3x2 = -2x Solving for variable 'x'. Reorder the terms: 9 + 14x + 2x + 3x2 = -2x + 2x Combine like terms: 14x + 2x = 16x 9 + 16x + 3x2 = -2x + 2x Combine like terms: -2x + 2x = 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 = 4.111111113 7.111111113 + 5.333333333x + x2 = 4.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 4.111111113 Calculate the square root of the right side: 2.027587511 Break this problem into two subproblems by setting (x + 2.666666667) equal to 2.027587511 and -2.027587511.Subproblem 1
x + 2.666666667 = 2.027587511 Simplifying x + 2.666666667 = 2.027587511 Reorder the terms: 2.666666667 + x = 2.027587511 Solving 2.666666667 + x = 2.027587511 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 = 2.027587511 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 2.027587511 + -2.666666667 x = 2.027587511 + -2.666666667 Combine like terms: 2.027587511 + -2.666666667 = -0.639079156 x = -0.639079156 Simplifying x = -0.639079156Subproblem 2
x + 2.666666667 = -2.027587511 Simplifying x + 2.666666667 = -2.027587511 Reorder the terms: 2.666666667 + x = -2.027587511 Solving 2.666666667 + x = -2.027587511 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 = -2.027587511 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -2.027587511 + -2.666666667 x = -2.027587511 + -2.666666667 Combine like terms: -2.027587511 + -2.666666667 = -4.694254178 x = -4.694254178 Simplifying x = -4.694254178Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.639079156, -4.694254178}
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