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Simplifying 12x + 3x2 = 16 Solving 12x + 3x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 12x + 3x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 4x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 4x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 4x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 4x + x2 = 0 + 5.333333333 4x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 4x + x2 = 5.333333333 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 = 5.333333333 + 4 Reorder the terms: 4 + 4x + x2 = 5.333333333 + 4 Combine like terms: 5.333333333 + 4 = 9.333333333 4 + 4x + x2 = 9.333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 9.333333333 Calculate the square root of the right side: 3.055050463 Break this problem into two subproblems by setting (x + 2) equal to 3.055050463 and -3.055050463.Subproblem 1
x + 2 = 3.055050463 Simplifying x + 2 = 3.055050463 Reorder the terms: 2 + x = 3.055050463 Solving 2 + x = 3.055050463 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 = 3.055050463 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.055050463 + -2 x = 3.055050463 + -2 Combine like terms: 3.055050463 + -2 = 1.055050463 x = 1.055050463 Simplifying x = 1.055050463Subproblem 2
x + 2 = -3.055050463 Simplifying x + 2 = -3.055050463 Reorder the terms: 2 + x = -3.055050463 Solving 2 + x = -3.055050463 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 = -3.055050463 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.055050463 + -2 x = -3.055050463 + -2 Combine like terms: -3.055050463 + -2 = -5.055050463 x = -5.055050463 Simplifying x = -5.055050463Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.055050463, -5.055050463}
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