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Simplifying 3x2 + 24x = 16 Reorder the terms: 24x + 3x2 = 16 Solving 24x + 3x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 24x + 3x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 24x + 3x2 = 0 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 = 0.618802153 x = 0.618802153 Simplifying x = 0.618802153Subproblem 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 = -8.618802153 x = -8.618802153 Simplifying x = -8.618802153Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.618802153, -8.618802153}
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