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Simplifying 18x2 + -1 = -1x Reorder the terms: -1 + 18x2 = -1x Solving -1 + 18x2 = -1x Solving for variable 'x'. Reorder the terms: -1 + x + 18x2 = -1x + x Combine like terms: -1x + x = 0 -1 + x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 0.05555555556x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 0.05555555556x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 0.05555555556x + x2 = 0 + 0.05555555556 0.05555555556x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 0.05555555556x + x2 = 0.05555555556 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. 0.05555555556x + 0.25 + x2 = 0.05555555556 + 0.25 Reorder the terms: 0.25 + 0.05555555556x + x2 = 0.05555555556 + 0.25 Combine like terms: 0.05555555556 + 0.25 = 0.30555555556 0.25 + 0.05555555556x + x2 = 0.30555555556 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.30555555556 Calculate the square root of the right side: 0.552770798 Break this problem into two subproblems by setting (x + 0.5) equal to 0.552770798 and -0.552770798.Subproblem 1
x + 0.5 = 0.552770798 Simplifying x + 0.5 = 0.552770798 Reorder the terms: 0.5 + x = 0.552770798 Solving 0.5 + x = 0.552770798 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 = 0.552770798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.552770798 + -0.5 x = 0.552770798 + -0.5 Combine like terms: 0.552770798 + -0.5 = 0.052770798 x = 0.052770798 Simplifying x = 0.052770798Subproblem 2
x + 0.5 = -0.552770798 Simplifying x + 0.5 = -0.552770798 Reorder the terms: 0.5 + x = -0.552770798 Solving 0.5 + x = -0.552770798 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 = -0.552770798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.552770798 + -0.5 x = -0.552770798 + -0.5 Combine like terms: -0.552770798 + -0.5 = -1.052770798 x = -1.052770798 Simplifying x = -1.052770798Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.052770798, -1.052770798}
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