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Simplifying 3x2 + x = 0.6666 Reorder the terms: x + 3x2 = 0.6666 Solving x + 3x2 = 0.6666 Solving for variable 'x'. Reorder the terms: -0.6666 + x + 3x2 = 0.6666 + -0.6666 Combine like terms: 0.6666 + -0.6666 = 0.0000 -0.6666 + x + 3x2 = 0.0000 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.2222 + 0.3333333333x + x2 = 0.0000 Move the constant term to the right: Add '0.2222' to each side of the equation. -0.2222 + 0.3333333333x + 0.2222 + x2 = 0.0000 + 0.2222 Reorder the terms: -0.2222 + 0.2222 + 0.3333333333x + x2 = 0.0000 + 0.2222 Combine like terms: -0.2222 + 0.2222 = 0.0000 0.0000 + 0.3333333333x + x2 = 0.0000 + 0.2222 0.3333333333x + x2 = 0.0000 + 0.2222 Combine like terms: 0.0000 + 0.2222 = 0.2222 0.3333333333x + x2 = 0.2222 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 = 0.2222 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 0.2222 + 0.25 Combine like terms: 0.2222 + 0.25 = 0.4722 0.25 + 0.3333333333x + x2 = 0.4722 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.4722 Calculate the square root of the right side: 0.687168102 Break this problem into two subproblems by setting (x + 0.5) equal to 0.687168102 and -0.687168102.Subproblem 1
x + 0.5 = 0.687168102 Simplifying x + 0.5 = 0.687168102 Reorder the terms: 0.5 + x = 0.687168102 Solving 0.5 + x = 0.687168102 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 = 0.687168102 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.687168102 + -0.5 x = 0.687168102 + -0.5 Combine like terms: 0.687168102 + -0.5 = 0.187168102 x = 0.187168102 Simplifying x = 0.187168102Subproblem 2
x + 0.5 = -0.687168102 Simplifying x + 0.5 = -0.687168102 Reorder the terms: 0.5 + x = -0.687168102 Solving 0.5 + x = -0.687168102 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 = -0.687168102 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.687168102 + -0.5 x = -0.687168102 + -0.5 Combine like terms: -0.687168102 + -0.5 = -1.187168102 x = -1.187168102 Simplifying x = -1.187168102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187168102, -1.187168102}
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