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Simplifying 3x2 + 12x + -16 = 96 Reorder the terms: -16 + 12x + 3x2 = 96 Solving -16 + 12x + 3x2 = 96 Solving for variable 'x'. Reorder the terms: -16 + -96 + 12x + 3x2 = 96 + -96 Combine like terms: -16 + -96 = -112 -112 + 12x + 3x2 = 96 + -96 Combine like terms: 96 + -96 = 0 -112 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -37.33333333 + 4x + x2 = 0 Move the constant term to the right: Add '37.33333333' to each side of the equation. -37.33333333 + 4x + 37.33333333 + x2 = 0 + 37.33333333 Reorder the terms: -37.33333333 + 37.33333333 + 4x + x2 = 0 + 37.33333333 Combine like terms: -37.33333333 + 37.33333333 = 0.00000000 0.00000000 + 4x + x2 = 0 + 37.33333333 4x + x2 = 0 + 37.33333333 Combine like terms: 0 + 37.33333333 = 37.33333333 4x + x2 = 37.33333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 37.33333333 + 4 Reorder the terms: 4 + 4x + x2 = 37.33333333 + 4 Combine like terms: 37.33333333 + 4 = 41.33333333 4 + 4x + x2 = 41.33333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 41.33333333 Calculate the square root of the right side: 6.429100507 Break this problem into two subproblems by setting (x + 2) equal to 6.429100507 and -6.429100507.Subproblem 1
x + 2 = 6.429100507 Simplifying x + 2 = 6.429100507 Reorder the terms: 2 + x = 6.429100507 Solving 2 + x = 6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.429100507 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.429100507 + -2 x = 6.429100507 + -2 Combine like terms: 6.429100507 + -2 = 4.429100507 x = 4.429100507 Simplifying x = 4.429100507Subproblem 2
x + 2 = -6.429100507 Simplifying x + 2 = -6.429100507 Reorder the terms: 2 + x = -6.429100507 Solving 2 + x = -6.429100507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.429100507 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.429100507 + -2 x = -6.429100507 + -2 Combine like terms: -6.429100507 + -2 = -8.429100507 x = -8.429100507 Simplifying x = -8.429100507Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.429100507, -8.429100507}
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