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Simplifying -3x2 = 16x + 12 Reorder the terms: -3x2 = 12 + 16x Solving -3x2 = 12 + 16x Solving for variable 'x'. Reorder the terms: -12 + -16x + -3x2 = 12 + 16x + -12 + -16x Reorder the terms: -12 + -16x + -3x2 = 12 + -12 + 16x + -16x Combine like terms: 12 + -12 = 0 -12 + -16x + -3x2 = 0 + 16x + -16x -12 + -16x + -3x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -12 + -16x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 16x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 16x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + 16x + 3x2 = 0 Solving 12 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 5.333333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 5.333333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5.333333333x + x2 = 0 + -4 5.333333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 5.333333333x + x2 = -4 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 = -4 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = -4 + 7.111111113 Combine like terms: -4 + 7.111111113 = 3.111111113 7.111111113 + 5.333333333x + x2 = 3.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 3.111111113 Calculate the square root of the right side: 1.763834208 Break this problem into two subproblems by setting (x + 2.666666667) equal to 1.763834208 and -1.763834208.Subproblem 1
x + 2.666666667 = 1.763834208 Simplifying x + 2.666666667 = 1.763834208 Reorder the terms: 2.666666667 + x = 1.763834208 Solving 2.666666667 + x = 1.763834208 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 = 1.763834208 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 1.763834208 + -2.666666667 x = 1.763834208 + -2.666666667 Combine like terms: 1.763834208 + -2.666666667 = -0.902832459 x = -0.902832459 Simplifying x = -0.902832459Subproblem 2
x + 2.666666667 = -1.763834208 Simplifying x + 2.666666667 = -1.763834208 Reorder the terms: 2.666666667 + x = -1.763834208 Solving 2.666666667 + x = -1.763834208 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 = -1.763834208 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -1.763834208 + -2.666666667 x = -1.763834208 + -2.666666667 Combine like terms: -1.763834208 + -2.666666667 = -4.430500875 x = -4.430500875 Simplifying x = -4.430500875Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.902832459, -4.430500875}Solution
x = {-0.902832459, -4.430500875}
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