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Simplifying 3x2 + -16x + -48 = 0 Reorder the terms: -48 + -16x + 3x2 = 0 Solving -48 + -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'. -16 + -5.333333333x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -5.333333333x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -5.333333333x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5.333333333x + x2 = 0 + 16 -5.333333333x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5.333333333x + x2 = 16 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 = 16 + 7.111111113 Reorder the terms: 7.111111113 + -5.333333333x + x2 = 16 + 7.111111113 Combine like terms: 16 + 7.111111113 = 23.111111113 7.111111113 + -5.333333333x + x2 = 23.111111113 Factor a perfect square on the left side: (x + -2.666666667)(x + -2.666666667) = 23.111111113 Calculate the square root of the right side: 4.807401701 Break this problem into two subproblems by setting (x + -2.666666667) equal to 4.807401701 and -4.807401701.Subproblem 1
x + -2.666666667 = 4.807401701 Simplifying x + -2.666666667 = 4.807401701 Reorder the terms: -2.666666667 + x = 4.807401701 Solving -2.666666667 + x = 4.807401701 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 = 4.807401701 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 4.807401701 + 2.666666667 x = 4.807401701 + 2.666666667 Combine like terms: 4.807401701 + 2.666666667 = 7.474068368 x = 7.474068368 Simplifying x = 7.474068368Subproblem 2
x + -2.666666667 = -4.807401701 Simplifying x + -2.666666667 = -4.807401701 Reorder the terms: -2.666666667 + x = -4.807401701 Solving -2.666666667 + x = -4.807401701 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 = -4.807401701 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -4.807401701 + 2.666666667 x = -4.807401701 + 2.666666667 Combine like terms: -4.807401701 + 2.666666667 = -2.140735034 x = -2.140735034 Simplifying x = -2.140735034Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.474068368, -2.140735034}
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