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Simplifying 3x2 = 19 + 6x Solving 3x2 = 19 + 6x Solving for variable 'x'. Reorder the terms: -19 + -6x + 3x2 = 19 + 6x + -19 + -6x Reorder the terms: -19 + -6x + 3x2 = 19 + -19 + 6x + -6x Combine like terms: 19 + -19 = 0 -19 + -6x + 3x2 = 0 + 6x + -6x -19 + -6x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -19 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -2x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -2x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 6.333333333 -2x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -2x + x2 = 6.333333333 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 = 6.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 6.333333333 + 1 Combine like terms: 6.333333333 + 1 = 7.333333333 1 + -2x + x2 = 7.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (x + -1) equal to 2.708012801 and -2.708012801.Subproblem 1
x + -1 = 2.708012801 Simplifying x + -1 = 2.708012801 Reorder the terms: -1 + x = 2.708012801 Solving -1 + x = 2.708012801 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 = 2.708012801 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.708012801 + 1 x = 2.708012801 + 1 Combine like terms: 2.708012801 + 1 = 3.708012801 x = 3.708012801 Simplifying x = 3.708012801Subproblem 2
x + -1 = -2.708012801 Simplifying x + -1 = -2.708012801 Reorder the terms: -1 + x = -2.708012801 Solving -1 + x = -2.708012801 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 = -2.708012801 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.708012801 + 1 x = -2.708012801 + 1 Combine like terms: -2.708012801 + 1 = -1.708012801 x = -1.708012801 Simplifying x = -1.708012801Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.708012801, -1.708012801}
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