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Simplifying 45x2 + 10x + -0.2 = 0 Reorder the terms: -0.2 + 10x + 45x2 = 0 Solving -0.2 + 10x + 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'. -0.004444444444 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.004444444444' to each side of the equation. -0.004444444444 + 0.2222222222x + 0.004444444444 + x2 = 0 + 0.004444444444 Reorder the terms: -0.004444444444 + 0.004444444444 + 0.2222222222x + x2 = 0 + 0.004444444444 Combine like terms: -0.004444444444 + 0.004444444444 = 0.000000000000 0.000000000000 + 0.2222222222x + x2 = 0 + 0.004444444444 0.2222222222x + x2 = 0 + 0.004444444444 Combine like terms: 0 + 0.004444444444 = 0.004444444444 0.2222222222x + x2 = 0.004444444444 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 0.004444444444 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.004444444444 + 0.01234567901 Combine like terms: 0.004444444444 + 0.01234567901 = 0.016790123454 0.01234567901 + 0.2222222222x + x2 = 0.016790123454 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.016790123454 Calculate the square root of the right side: 0.129576709 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.129576709 and -0.129576709.Subproblem 1
x + 0.1111111111 = 0.129576709 Simplifying x + 0.1111111111 = 0.129576709 Reorder the terms: 0.1111111111 + x = 0.129576709 Solving 0.1111111111 + x = 0.129576709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 0.129576709 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.129576709 + -0.1111111111 x = 0.129576709 + -0.1111111111 Combine like terms: 0.129576709 + -0.1111111111 = 0.0184655979 x = 0.0184655979 Simplifying x = 0.0184655979Subproblem 2
x + 0.1111111111 = -0.129576709 Simplifying x + 0.1111111111 = -0.129576709 Reorder the terms: 0.1111111111 + x = -0.129576709 Solving 0.1111111111 + x = -0.129576709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -0.129576709 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.129576709 + -0.1111111111 x = -0.129576709 + -0.1111111111 Combine like terms: -0.129576709 + -0.1111111111 = -0.2406878201 x = -0.2406878201 Simplifying x = -0.2406878201Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0184655979, -0.2406878201}
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