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Simplifying 81x2 + 18x + -4 = 0 Reorder the terms: -4 + 18x + 81x2 = 0 Solving -4 + 18x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.04938271605 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '0.04938271605' to each side of the equation. -0.04938271605 + 0.2222222222x + 0.04938271605 + x2 = 0 + 0.04938271605 Reorder the terms: -0.04938271605 + 0.04938271605 + 0.2222222222x + x2 = 0 + 0.04938271605 Combine like terms: -0.04938271605 + 0.04938271605 = 0.00000000000 0.00000000000 + 0.2222222222x + x2 = 0 + 0.04938271605 0.2222222222x + x2 = 0 + 0.04938271605 Combine like terms: 0 + 0.04938271605 = 0.04938271605 0.2222222222x + x2 = 0.04938271605 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 = 0.04938271605 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 0.04938271605 + 0.01234567901 Combine like terms: 0.04938271605 + 0.01234567901 = 0.06172839506 0.01234567901 + 0.2222222222x + x2 = 0.06172839506 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 0.06172839506 Calculate the square root of the right side: 0.248451997 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 0.248451997 and -0.248451997.Subproblem 1
x + 0.1111111111 = 0.248451997 Simplifying x + 0.1111111111 = 0.248451997 Reorder the terms: 0.1111111111 + x = 0.248451997 Solving 0.1111111111 + x = 0.248451997 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 = 0.248451997 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.248451997 + -0.1111111111 x = 0.248451997 + -0.1111111111 Combine like terms: 0.248451997 + -0.1111111111 = 0.1373408859 x = 0.1373408859 Simplifying x = 0.1373408859Subproblem 2
x + 0.1111111111 = -0.248451997 Simplifying x + 0.1111111111 = -0.248451997 Reorder the terms: 0.1111111111 + x = -0.248451997 Solving 0.1111111111 + x = -0.248451997 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 = -0.248451997 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.248451997 + -0.1111111111 x = -0.248451997 + -0.1111111111 Combine like terms: -0.248451997 + -0.1111111111 = -0.3595631081 x = -0.3595631081 Simplifying x = -0.3595631081Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1373408859, -0.3595631081}
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