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Simplifying 3x + 1 = 3x2 + -12x + -15 Reorder the terms: 1 + 3x = 3x2 + -12x + -15 Reorder the terms: 1 + 3x = -15 + -12x + 3x2 Solving 1 + 3x = -15 + -12x + 3x2 Solving for variable 'x'. Reorder the terms: 1 + 15 + 3x + 12x + -3x2 = -15 + -12x + 3x2 + 15 + 12x + -3x2 Combine like terms: 1 + 15 = 16 16 + 3x + 12x + -3x2 = -15 + -12x + 3x2 + 15 + 12x + -3x2 Combine like terms: 3x + 12x = 15x 16 + 15x + -3x2 = -15 + -12x + 3x2 + 15 + 12x + -3x2 Reorder the terms: 16 + 15x + -3x2 = -15 + 15 + -12x + 12x + 3x2 + -3x2 Combine like terms: -15 + 15 = 0 16 + 15x + -3x2 = 0 + -12x + 12x + 3x2 + -3x2 16 + 15x + -3x2 = -12x + 12x + 3x2 + -3x2 Combine like terms: -12x + 12x = 0 16 + 15x + -3x2 = 0 + 3x2 + -3x2 16 + 15x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 16 + 15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5.333333333 + -5x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -5x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -5x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + 5.333333333 -5x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -5x + x2 = 5.333333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 5.333333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 5.333333333 + 6.25 Combine like terms: 5.333333333 + 6.25 = 11.583333333 6.25 + -5x + x2 = 11.583333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 11.583333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (x + -2.5) equal to 3.403429643 and -3.403429643.Subproblem 1
x + -2.5 = 3.403429643 Simplifying x + -2.5 = 3.403429643 Reorder the terms: -2.5 + x = 3.403429643 Solving -2.5 + x = 3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.403429643 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.403429643 + 2.5 x = 3.403429643 + 2.5 Combine like terms: 3.403429643 + 2.5 = 5.903429643 x = 5.903429643 Simplifying x = 5.903429643Subproblem 2
x + -2.5 = -3.403429643 Simplifying x + -2.5 = -3.403429643 Reorder the terms: -2.5 + x = -3.403429643 Solving -2.5 + x = -3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.403429643 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.403429643 + 2.5 x = -3.403429643 + 2.5 Combine like terms: -3.403429643 + 2.5 = -0.903429643 x = -0.903429643 Simplifying x = -0.903429643Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.903429643, -0.903429643}
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