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Simplifying 18x2 + -17x + 1 = 0 Reorder the terms: 1 + -17x + 18x2 = 0 Solving 1 + -17x + 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 + -0.9444444444x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -0.9444444444x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -0.9444444444x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -0.9444444444x + x2 = 0 + -0.05555555556 -0.9444444444x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -0.9444444444x + x2 = -0.05555555556 The x term is -0.9444444444x. Take half its coefficient (-0.4722222222). Square it (0.2229938271) and add it to both sides. Add '0.2229938271' to each side of the equation. -0.9444444444x + 0.2229938271 + x2 = -0.05555555556 + 0.2229938271 Reorder the terms: 0.2229938271 + -0.9444444444x + x2 = -0.05555555556 + 0.2229938271 Combine like terms: -0.05555555556 + 0.2229938271 = 0.16743827154 0.2229938271 + -0.9444444444x + x2 = 0.16743827154 Factor a perfect square on the left side: (x + -0.4722222222)(x + -0.4722222222) = 0.16743827154 Calculate the square root of the right side: 0.409192218 Break this problem into two subproblems by setting (x + -0.4722222222) equal to 0.409192218 and -0.409192218.Subproblem 1
x + -0.4722222222 = 0.409192218 Simplifying x + -0.4722222222 = 0.409192218 Reorder the terms: -0.4722222222 + x = 0.409192218 Solving -0.4722222222 + x = 0.409192218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4722222222' to each side of the equation. -0.4722222222 + 0.4722222222 + x = 0.409192218 + 0.4722222222 Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000 0.0000000000 + x = 0.409192218 + 0.4722222222 x = 0.409192218 + 0.4722222222 Combine like terms: 0.409192218 + 0.4722222222 = 0.8814144402 x = 0.8814144402 Simplifying x = 0.8814144402Subproblem 2
x + -0.4722222222 = -0.409192218 Simplifying x + -0.4722222222 = -0.409192218 Reorder the terms: -0.4722222222 + x = -0.409192218 Solving -0.4722222222 + x = -0.409192218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4722222222' to each side of the equation. -0.4722222222 + 0.4722222222 + x = -0.409192218 + 0.4722222222 Combine like terms: -0.4722222222 + 0.4722222222 = 0.0000000000 0.0000000000 + x = -0.409192218 + 0.4722222222 x = -0.409192218 + 0.4722222222 Combine like terms: -0.409192218 + 0.4722222222 = 0.0630300042 x = 0.0630300042 Simplifying x = 0.0630300042Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8814144402, 0.0630300042}
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