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Simplifying 90x2 + x + 1 = 0 Reorder the terms: 1 + x + 90x2 = 0 Solving 1 + x + 90x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. 0.01111111111 + 0.01111111111x + x2 = 0 Move the constant term to the right: Add '-0.01111111111' to each side of the equation. 0.01111111111 + 0.01111111111x + -0.01111111111 + x2 = 0 + -0.01111111111 Reorder the terms: 0.01111111111 + -0.01111111111 + 0.01111111111x + x2 = 0 + -0.01111111111 Combine like terms: 0.01111111111 + -0.01111111111 = 0.00000000000 0.00000000000 + 0.01111111111x + x2 = 0 + -0.01111111111 0.01111111111x + x2 = 0 + -0.01111111111 Combine like terms: 0 + -0.01111111111 = -0.01111111111 0.01111111111x + x2 = -0.01111111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.01111111111x + 0.25 + x2 = -0.01111111111 + 0.25 Reorder the terms: 0.25 + 0.01111111111x + x2 = -0.01111111111 + 0.25 Combine like terms: -0.01111111111 + 0.25 = 0.23888888889 0.25 + 0.01111111111x + x2 = 0.23888888889 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.23888888889 Calculate the square root of the right side: 0.48876261 Break this problem into two subproblems by setting (x + 0.5) equal to 0.48876261 and -0.48876261.Subproblem 1
x + 0.5 = 0.48876261 Simplifying x + 0.5 = 0.48876261 Reorder the terms: 0.5 + x = 0.48876261 Solving 0.5 + x = 0.48876261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.48876261 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.48876261 + -0.5 x = 0.48876261 + -0.5 Combine like terms: 0.48876261 + -0.5 = -0.01123739 x = -0.01123739 Simplifying x = -0.01123739Subproblem 2
x + 0.5 = -0.48876261 Simplifying x + 0.5 = -0.48876261 Reorder the terms: 0.5 + x = -0.48876261 Solving 0.5 + x = -0.48876261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.48876261 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.48876261 + -0.5 x = -0.48876261 + -0.5 Combine like terms: -0.48876261 + -0.5 = -0.98876261 x = -0.98876261 Simplifying x = -0.98876261Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.01123739, -0.98876261}
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