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Simplifying 3x2 + x = 0.66 Reorder the terms: x + 3x2 = 0.66 Solving x + 3x2 = 0.66 Solving for variable 'x'. Reorder the terms: -0.66 + x + 3x2 = 0.66 + -0.66 Combine like terms: 0.66 + -0.66 = 0.00 -0.66 + x + 3x2 = 0.00 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.22 + 0.3333333333x + x2 = 0.00 Move the constant term to the right: Add '0.22' to each side of the equation. -0.22 + 0.3333333333x + 0.22 + x2 = 0.00 + 0.22 Reorder the terms: -0.22 + 0.22 + 0.3333333333x + x2 = 0.00 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + 0.3333333333x + x2 = 0.00 + 0.22 0.3333333333x + x2 = 0.00 + 0.22 Combine like terms: 0.00 + 0.22 = 0.22 0.3333333333x + x2 = 0.22 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 = 0.22 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 0.22 + 0.25 Combine like terms: 0.22 + 0.25 = 0.47 0.25 + 0.3333333333x + x2 = 0.47 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.47 Calculate the square root of the right side: 0.68556546 Break this problem into two subproblems by setting (x + 0.5) equal to 0.68556546 and -0.68556546.Subproblem 1
x + 0.5 = 0.68556546 Simplifying x + 0.5 = 0.68556546 Reorder the terms: 0.5 + x = 0.68556546 Solving 0.5 + x = 0.68556546 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 = 0.68556546 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.68556546 + -0.5 x = 0.68556546 + -0.5 Combine like terms: 0.68556546 + -0.5 = 0.18556546 x = 0.18556546 Simplifying x = 0.18556546Subproblem 2
x + 0.5 = -0.68556546 Simplifying x + 0.5 = -0.68556546 Reorder the terms: 0.5 + x = -0.68556546 Solving 0.5 + x = -0.68556546 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 = -0.68556546 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.68556546 + -0.5 x = -0.68556546 + -0.5 Combine like terms: -0.68556546 + -0.5 = -1.18556546 x = -1.18556546 Simplifying x = -1.18556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.18556546, -1.18556546}
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