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Simplifying 3x2 + -3x + -12 = 3x + 16 Reorder the terms: -12 + -3x + 3x2 = 3x + 16 Reorder the terms: -12 + -3x + 3x2 = 16 + 3x Solving -12 + -3x + 3x2 = 16 + 3x Solving for variable 'x'. Reorder the terms: -12 + -16 + -3x + -3x + 3x2 = 16 + 3x + -16 + -3x Combine like terms: -12 + -16 = -28 -28 + -3x + -3x + 3x2 = 16 + 3x + -16 + -3x Combine like terms: -3x + -3x = -6x -28 + -6x + 3x2 = 16 + 3x + -16 + -3x Reorder the terms: -28 + -6x + 3x2 = 16 + -16 + 3x + -3x Combine like terms: 16 + -16 = 0 -28 + -6x + 3x2 = 0 + 3x + -3x -28 + -6x + 3x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -28 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '9.333333333' to each side of the equation. -9.333333333 + -2x + 9.333333333 + x2 = 0 + 9.333333333 Reorder the terms: -9.333333333 + 9.333333333 + -2x + x2 = 0 + 9.333333333 Combine like terms: -9.333333333 + 9.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 9.333333333 -2x + x2 = 0 + 9.333333333 Combine like terms: 0 + 9.333333333 = 9.333333333 -2x + x2 = 9.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 9.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 9.333333333 + 1 Combine like terms: 9.333333333 + 1 = 10.333333333 1 + -2x + x2 = 10.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 10.333333333 Calculate the square root of the right side: 3.214550254 Break this problem into two subproblems by setting (x + -1) equal to 3.214550254 and -3.214550254.Subproblem 1
x + -1 = 3.214550254 Simplifying x + -1 = 3.214550254 Reorder the terms: -1 + x = 3.214550254 Solving -1 + x = 3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.214550254 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.214550254 + 1 x = 3.214550254 + 1 Combine like terms: 3.214550254 + 1 = 4.214550254 x = 4.214550254 Simplifying x = 4.214550254Subproblem 2
x + -1 = -3.214550254 Simplifying x + -1 = -3.214550254 Reorder the terms: -1 + x = -3.214550254 Solving -1 + x = -3.214550254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.214550254 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.214550254 + 1 x = -3.214550254 + 1 Combine like terms: -3.214550254 + 1 = -2.214550254 x = -2.214550254 Simplifying x = -2.214550254Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.214550254, -2.214550254}
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