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Simplifying 45x2 + 6x + -2 = 0 Reorder the terms: -2 + 6x + 45x2 = 0 Solving -2 + 6x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.04444444444 + 0.1333333333x + x2 = 0 Move the constant term to the right: Add '0.04444444444' to each side of the equation. -0.04444444444 + 0.1333333333x + 0.04444444444 + x2 = 0 + 0.04444444444 Reorder the terms: -0.04444444444 + 0.04444444444 + 0.1333333333x + x2 = 0 + 0.04444444444 Combine like terms: -0.04444444444 + 0.04444444444 = 0.00000000000 0.00000000000 + 0.1333333333x + x2 = 0 + 0.04444444444 0.1333333333x + x2 = 0 + 0.04444444444 Combine like terms: 0 + 0.04444444444 = 0.04444444444 0.1333333333x + x2 = 0.04444444444 The x term is 0.1333333333x. Take half its coefficient (0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. 0.1333333333x + 0.004444444442 + x2 = 0.04444444444 + 0.004444444442 Reorder the terms: 0.004444444442 + 0.1333333333x + x2 = 0.04444444444 + 0.004444444442 Combine like terms: 0.04444444444 + 0.004444444442 = 0.048888888882 0.004444444442 + 0.1333333333x + x2 = 0.048888888882 Factor a perfect square on the left side: (x + 0.06666666665)(x + 0.06666666665) = 0.048888888882 Calculate the square root of the right side: 0.221108319 Break this problem into two subproblems by setting (x + 0.06666666665) equal to 0.221108319 and -0.221108319.Subproblem 1
x + 0.06666666665 = 0.221108319 Simplifying x + 0.06666666665 = 0.221108319 Reorder the terms: 0.06666666665 + x = 0.221108319 Solving 0.06666666665 + x = 0.221108319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = 0.221108319 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = 0.221108319 + -0.06666666665 x = 0.221108319 + -0.06666666665 Combine like terms: 0.221108319 + -0.06666666665 = 0.15444165235 x = 0.15444165235 Simplifying x = 0.15444165235Subproblem 2
x + 0.06666666665 = -0.221108319 Simplifying x + 0.06666666665 = -0.221108319 Reorder the terms: 0.06666666665 + x = -0.221108319 Solving 0.06666666665 + x = -0.221108319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.06666666665' to each side of the equation. 0.06666666665 + -0.06666666665 + x = -0.221108319 + -0.06666666665 Combine like terms: 0.06666666665 + -0.06666666665 = 0.00000000000 0.00000000000 + x = -0.221108319 + -0.06666666665 x = -0.221108319 + -0.06666666665 Combine like terms: -0.221108319 + -0.06666666665 = -0.28777498565 x = -0.28777498565 Simplifying x = -0.28777498565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.15444165235, -0.28777498565}
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