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Simplifying 18x2 + 2x = 0.08 Reorder the terms: 2x + 18x2 = 0.08 Solving 2x + 18x2 = 0.08 Solving for variable 'x'. Reorder the terms: -0.08 + 2x + 18x2 = 0.08 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 -0.08 + 2x + 18x2 = 0.00 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.004444444444 + 0.1111111111x + x2 = 0.00 Move the constant term to the right: Add '0.004444444444' to each side of the equation. -0.004444444444 + 0.1111111111x + 0.004444444444 + x2 = 0.00 + 0.004444444444 Reorder the terms: -0.004444444444 + 0.004444444444 + 0.1111111111x + x2 = 0.00 + 0.004444444444 Combine like terms: -0.004444444444 + 0.004444444444 = 0.000000000000 0.000000000000 + 0.1111111111x + x2 = 0.00 + 0.004444444444 0.1111111111x + x2 = 0.00 + 0.004444444444 Combine like terms: 0.00 + 0.004444444444 = 0.004444444444 0.1111111111x + x2 = 0.004444444444 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = 0.004444444444 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.004444444444 + 0.003086419752 Combine like terms: 0.004444444444 + 0.003086419752 = 0.007530864196 0.003086419752 + 0.1111111111x + x2 = 0.007530864196 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.007530864196 Calculate the square root of the right side: 0.086780552 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.086780552 and -0.086780552.Subproblem 1
x + 0.05555555555 = 0.086780552 Simplifying x + 0.05555555555 = 0.086780552 Reorder the terms: 0.05555555555 + x = 0.086780552 Solving 0.05555555555 + x = 0.086780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 0.086780552 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.086780552 + -0.05555555555 x = 0.086780552 + -0.05555555555 Combine like terms: 0.086780552 + -0.05555555555 = 0.03122499645 x = 0.03122499645 Simplifying x = 0.03122499645Subproblem 2
x + 0.05555555555 = -0.086780552 Simplifying x + 0.05555555555 = -0.086780552 Reorder the terms: 0.05555555555 + x = -0.086780552 Solving 0.05555555555 + x = -0.086780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -0.086780552 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.086780552 + -0.05555555555 x = -0.086780552 + -0.05555555555 Combine like terms: -0.086780552 + -0.05555555555 = -0.14233610755 x = -0.14233610755 Simplifying x = -0.14233610755Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03122499645, -0.14233610755}
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