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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 = 10.666666667 16 + 8x + x2 = 10.666666667 Factor a perfect square on the left side: (x + 4)(x + 4) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x + 4) equal to 3.265986324 and -3.265986324.Subproblem 1
x + 4 = 3.265986324 Simplifying x + 4 = 3.265986324 Reorder the terms: 4 + x = 3.265986324 Solving 4 + x = 3.265986324 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 = 3.265986324 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.265986324 + -4 x = 3.265986324 + -4 Combine like terms: 3.265986324 + -4 = -0.734013676 x = -0.734013676 Simplifying x = -0.734013676Subproblem 2
x + 4 = -3.265986324 Simplifying x + 4 = -3.265986324 Reorder the terms: 4 + x = -3.265986324 Solving 4 + x = -3.265986324 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 = -3.265986324 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.265986324 + -4 x = -3.265986324 + -4 Combine like terms: -3.265986324 + -4 = -7.265986324 x = -7.265986324 Simplifying x = -7.265986324Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.734013676, -7.265986324}
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