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Simplifying 3x2 + x + -0.33 = 0 Reorder the terms: -0.33 + x + 3x2 = 0 Solving -0.33 + x + 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'. -0.11 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.11' to each side of the equation. -0.11 + 0.3333333333x + 0.11 + x2 = 0 + 0.11 Reorder the terms: -0.11 + 0.11 + 0.3333333333x + x2 = 0 + 0.11 Combine like terms: -0.11 + 0.11 = 0.00 0.00 + 0.3333333333x + x2 = 0 + 0.11 0.3333333333x + x2 = 0 + 0.11 Combine like terms: 0 + 0.11 = 0.11 0.3333333333x + x2 = 0.11 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 0.11 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 0.11 + 0.25 Combine like terms: 0.11 + 0.25 = 0.36 0.25 + 0.3333333333x + x2 = 0.36 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.36 Calculate the square root of the right side: 0.6 Break this problem into two subproblems by setting (x + 0.5) equal to 0.6 and -0.6.Subproblem 1
x + 0.5 = 0.6 Simplifying x + 0.5 = 0.6 Reorder the terms: 0.5 + x = 0.6 Solving 0.5 + x = 0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.6 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.6 + -0.5 x = 0.6 + -0.5 Combine like terms: 0.6 + -0.5 = 0.1 x = 0.1 Simplifying x = 0.1Subproblem 2
x + 0.5 = -0.6 Simplifying x + 0.5 = -0.6 Reorder the terms: 0.5 + x = -0.6 Solving 0.5 + x = -0.6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.6 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.6 + -0.5 x = -0.6 + -0.5 Combine like terms: -0.6 + -0.5 = -1.1 x = -1.1 Simplifying x = -1.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1, -1.1}
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