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Simplifying 3x2 + 6x + -47 = 8 Reorder the terms: -47 + 6x + 3x2 = 8 Solving -47 + 6x + 3x2 = 8 Solving for variable 'x'. Reorder the terms: -47 + -8 + 6x + 3x2 = 8 + -8 Combine like terms: -47 + -8 = -55 -55 + 6x + 3x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -55 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -18.33333333 + 2x + x2 = 0 Move the constant term to the right: Add '18.33333333' to each side of the equation. -18.33333333 + 2x + 18.33333333 + x2 = 0 + 18.33333333 Reorder the terms: -18.33333333 + 18.33333333 + 2x + x2 = 0 + 18.33333333 Combine like terms: -18.33333333 + 18.33333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 18.33333333 2x + x2 = 0 + 18.33333333 Combine like terms: 0 + 18.33333333 = 18.33333333 2x + x2 = 18.33333333 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 = 18.33333333 + 1 Reorder the terms: 1 + 2x + x2 = 18.33333333 + 1 Combine like terms: 18.33333333 + 1 = 19.33333333 1 + 2x + x2 = 19.33333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 19.33333333 Calculate the square root of the right side: 4.396968652 Break this problem into two subproblems by setting (x + 1) equal to 4.396968652 and -4.396968652.Subproblem 1
x + 1 = 4.396968652 Simplifying x + 1 = 4.396968652 Reorder the terms: 1 + x = 4.396968652 Solving 1 + x = 4.396968652 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 = 4.396968652 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.396968652 + -1 x = 4.396968652 + -1 Combine like terms: 4.396968652 + -1 = 3.396968652 x = 3.396968652 Simplifying x = 3.396968652Subproblem 2
x + 1 = -4.396968652 Simplifying x + 1 = -4.396968652 Reorder the terms: 1 + x = -4.396968652 Solving 1 + x = -4.396968652 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 = -4.396968652 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.396968652 + -1 x = -4.396968652 + -1 Combine like terms: -4.396968652 + -1 = -5.396968652 x = -5.396968652 Simplifying x = -5.396968652Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.396968652, -5.396968652}
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