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Simplifying 36x2 + 8x + -3 = 0 Reorder the terms: -3 + 8x + 36x2 = 0 Solving -3 + 8x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.08333333333 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.2222222222x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.2222222222x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.2222222222x + x2 = 0 + 0.08333333333 0.2222222222x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.2222222222x + x2 = 0.08333333333 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 = 0.08333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.08333333333 + 0.01234567901 Combine like terms: 0.08333333333 + 0.01234567901 = 0.09567901234 0.01234567901 + 0.2222222222x + x2 = 0.09567901234 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.09567901234 Calculate the square root of the right side: 0.309320242 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.309320242 and -0.309320242.Subproblem 1
x + 0.1111111111 = 0.309320242 Simplifying x + 0.1111111111 = 0.309320242 Reorder the terms: 0.1111111111 + x = 0.309320242 Solving 0.1111111111 + x = 0.309320242 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 = 0.309320242 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.309320242 + -0.1111111111 x = 0.309320242 + -0.1111111111 Combine like terms: 0.309320242 + -0.1111111111 = 0.1982091309 x = 0.1982091309 Simplifying x = 0.1982091309Subproblem 2
x + 0.1111111111 = -0.309320242 Simplifying x + 0.1111111111 = -0.309320242 Reorder the terms: 0.1111111111 + x = -0.309320242 Solving 0.1111111111 + x = -0.309320242 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 = -0.309320242 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.309320242 + -0.1111111111 x = -0.309320242 + -0.1111111111 Combine like terms: -0.309320242 + -0.1111111111 = -0.4204313531 x = -0.4204313531 Simplifying x = -0.4204313531Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1982091309, -0.4204313531}
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