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Simplifying 0 = 18x2 + -18x + 1 Reorder the terms: 0 = 1 + -18x + 18x2 Solving 0 = 1 + -18x + 18x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 18x + -18x2 = 1 + -18x + 18x2 + -1 + 18x + -18x2 Reorder the terms: -1 + 18x + -18x2 = 1 + -1 + -18x + 18x + 18x2 + -18x2 Combine like terms: 1 + -1 = 0 -1 + 18x + -18x2 = 0 + -18x + 18x + 18x2 + -18x2 -1 + 18x + -18x2 = -18x + 18x + 18x2 + -18x2 Combine like terms: -18x + 18x = 0 -1 + 18x + -18x2 = 0 + 18x2 + -18x2 -1 + 18x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -1 + 18x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. 0.05555555556 + -1x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -1x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -1x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -1x + x2 = 0 + -0.05555555556 -1x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -1x + x2 = -0.05555555556 The x term is -1x. 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. -1x + 0.25 + x2 = -0.05555555556 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.05555555556 + 0.25 Combine like terms: -0.05555555556 + 0.25 = 0.19444444444 0.25 + -1x + x2 = 0.19444444444 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.19444444444 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + -0.5) equal to 0.440958552 and -0.440958552.Subproblem 1
x + -0.5 = 0.440958552 Simplifying x + -0.5 = 0.440958552 Reorder the terms: -0.5 + x = 0.440958552 Solving -0.5 + x = 0.440958552 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 = 0.440958552 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.440958552 + 0.5 x = 0.440958552 + 0.5 Combine like terms: 0.440958552 + 0.5 = 0.940958552 x = 0.940958552 Simplifying x = 0.940958552Subproblem 2
x + -0.5 = -0.440958552 Simplifying x + -0.5 = -0.440958552 Reorder the terms: -0.5 + x = -0.440958552 Solving -0.5 + x = -0.440958552 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 = -0.440958552 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.440958552 + 0.5 x = -0.440958552 + 0.5 Combine like terms: -0.440958552 + 0.5 = 0.059041448 x = 0.059041448 Simplifying x = 0.059041448Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.940958552, 0.059041448}
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