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Simplifying 3x2 + -24x + -16 = 0 Reorder the terms: -16 + -24x + 3x2 = 0 Solving -16 + -24x + 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'. -5.333333333 + -8x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -8x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -8x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -8x + x2 = 0 + 5.333333333 -8x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -8x + x2 = 5.333333333 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 5.333333333 + 16 Reorder the terms: 16 + -8x + x2 = 5.333333333 + 16 Combine like terms: 5.333333333 + 16 = 21.333333333 16 + -8x + x2 = 21.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 21.333333333 Calculate the square root of the right side: 4.618802153 Break this problem into two subproblems by setting (x + -4) equal to 4.618802153 and -4.618802153.Subproblem 1
x + -4 = 4.618802153 Simplifying x + -4 = 4.618802153 Reorder the terms: -4 + x = 4.618802153 Solving -4 + x = 4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.618802153 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.618802153 + 4 x = 4.618802153 + 4 Combine like terms: 4.618802153 + 4 = 8.618802153 x = 8.618802153 Simplifying x = 8.618802153Subproblem 2
x + -4 = -4.618802153 Simplifying x + -4 = -4.618802153 Reorder the terms: -4 + x = -4.618802153 Solving -4 + x = -4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.618802153 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.618802153 + 4 x = -4.618802153 + 4 Combine like terms: -4.618802153 + 4 = -0.618802153 x = -0.618802153 Simplifying x = -0.618802153Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.618802153, -0.618802153}
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