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Simplifying 3x2 + 33x + -6.7 = 0 Reorder the terms: -6.7 + 33x + 3x2 = 0 Solving -6.7 + 33x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.233333333 + 11x + x2 = 0 Move the constant term to the right: Add '2.233333333' to each side of the equation. -2.233333333 + 11x + 2.233333333 + x2 = 0 + 2.233333333 Reorder the terms: -2.233333333 + 2.233333333 + 11x + x2 = 0 + 2.233333333 Combine like terms: -2.233333333 + 2.233333333 = 0.000000000 0.000000000 + 11x + x2 = 0 + 2.233333333 11x + x2 = 0 + 2.233333333 Combine like terms: 0 + 2.233333333 = 2.233333333 11x + x2 = 2.233333333 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 2.233333333 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 2.233333333 + 30.25 Combine like terms: 2.233333333 + 30.25 = 32.483333333 30.25 + 11x + x2 = 32.483333333 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 32.483333333 Calculate the square root of the right side: 5.699415175 Break this problem into two subproblems by setting (x + 5.5) equal to 5.699415175 and -5.699415175.Subproblem 1
x + 5.5 = 5.699415175 Simplifying x + 5.5 = 5.699415175 Reorder the terms: 5.5 + x = 5.699415175 Solving 5.5 + x = 5.699415175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 5.699415175 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 5.699415175 + -5.5 x = 5.699415175 + -5.5 Combine like terms: 5.699415175 + -5.5 = 0.199415175 x = 0.199415175 Simplifying x = 0.199415175Subproblem 2
x + 5.5 = -5.699415175 Simplifying x + 5.5 = -5.699415175 Reorder the terms: 5.5 + x = -5.699415175 Solving 5.5 + x = -5.699415175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -5.699415175 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -5.699415175 + -5.5 x = -5.699415175 + -5.5 Combine like terms: -5.699415175 + -5.5 = -11.199415175 x = -11.199415175 Simplifying x = -11.199415175Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.199415175, -11.199415175}
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