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Simplifying 18x2 + 8x + -1 = 0 Reorder the terms: -1 + 8x + 18x2 = 0 Solving -1 + 8x + 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'. -0.05555555556 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.4444444444x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.4444444444x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.4444444444x + x2 = 0 + 0.05555555556 0.4444444444x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.4444444444x + x2 = 0.05555555556 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 0.05555555556 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 0.05555555556 + 0.04938271604 Combine like terms: 0.05555555556 + 0.04938271604 = 0.1049382716 0.04938271604 + 0.4444444444x + x2 = 0.1049382716 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.1049382716 Calculate the square root of the right side: 0.323941772 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.323941772 and -0.323941772.Subproblem 1
x + 0.2222222222 = 0.323941772 Simplifying x + 0.2222222222 = 0.323941772 Reorder the terms: 0.2222222222 + x = 0.323941772 Solving 0.2222222222 + x = 0.323941772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.323941772 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.323941772 + -0.2222222222 x = 0.323941772 + -0.2222222222 Combine like terms: 0.323941772 + -0.2222222222 = 0.1017195498 x = 0.1017195498 Simplifying x = 0.1017195498Subproblem 2
x + 0.2222222222 = -0.323941772 Simplifying x + 0.2222222222 = -0.323941772 Reorder the terms: 0.2222222222 + x = -0.323941772 Solving 0.2222222222 + x = -0.323941772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.323941772 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.323941772 + -0.2222222222 x = -0.323941772 + -0.2222222222 Combine like terms: -0.323941772 + -0.2222222222 = -0.5461639942 x = -0.5461639942 Simplifying x = -0.5461639942Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1017195498, -0.5461639942}
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