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Simplifying 18x2 + 9x + -4 = 0 Reorder the terms: -4 + 9x + 18x2 = 0 Solving -4 + 9x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.2222222222 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.5x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 0.5x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 0.5x + x2 = 0 + 0.2222222222 0.5x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 0.5x + x2 = 0.2222222222 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.2222222222 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.2222222222 + 0.0625 Combine like terms: 0.2222222222 + 0.0625 = 0.2847222222 0.0625 + 0.5x + x2 = 0.2847222222 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.2847222222 Calculate the square root of the right side: 0.533593686 Break this problem into two subproblems by setting (x + 0.25) equal to 0.533593686 and -0.533593686.Subproblem 1
x + 0.25 = 0.533593686 Simplifying x + 0.25 = 0.533593686 Reorder the terms: 0.25 + x = 0.533593686 Solving 0.25 + x = 0.533593686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.533593686 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.533593686 + -0.25 x = 0.533593686 + -0.25 Combine like terms: 0.533593686 + -0.25 = 0.283593686 x = 0.283593686 Simplifying x = 0.283593686Subproblem 2
x + 0.25 = -0.533593686 Simplifying x + 0.25 = -0.533593686 Reorder the terms: 0.25 + x = -0.533593686 Solving 0.25 + x = -0.533593686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.533593686 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.533593686 + -0.25 x = -0.533593686 + -0.25 Combine like terms: -0.533593686 + -0.25 = -0.783593686 x = -0.783593686 Simplifying x = -0.783593686Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283593686, -0.783593686}
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