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Simplifying 18x2 + -35x + 1 = 0 Reorder the terms: 1 + -35x + 18x2 = 0 Solving 1 + -35x + 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 + -1.944444444x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + -1.944444444x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + -1.944444444x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + -1.944444444x + x2 = 0 + -0.05555555556 -1.944444444x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 -1.944444444x + x2 = -0.05555555556 The x term is -1.944444444x. Take half its coefficient (-0.972222222). Square it (0.9452160490) and add it to both sides. Add '0.9452160490' to each side of the equation. -1.944444444x + 0.9452160490 + x2 = -0.05555555556 + 0.9452160490 Reorder the terms: 0.9452160490 + -1.944444444x + x2 = -0.05555555556 + 0.9452160490 Combine like terms: -0.05555555556 + 0.9452160490 = 0.88966049344 0.9452160490 + -1.944444444x + x2 = 0.88966049344 Factor a perfect square on the left side: (x + -0.972222222)(x + -0.972222222) = 0.88966049344 Calculate the square root of the right side: 0.943218158 Break this problem into two subproblems by setting (x + -0.972222222) equal to 0.943218158 and -0.943218158.Subproblem 1
x + -0.972222222 = 0.943218158 Simplifying x + -0.972222222 = 0.943218158 Reorder the terms: -0.972222222 + x = 0.943218158 Solving -0.972222222 + x = 0.943218158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.972222222' to each side of the equation. -0.972222222 + 0.972222222 + x = 0.943218158 + 0.972222222 Combine like terms: -0.972222222 + 0.972222222 = 0.000000000 0.000000000 + x = 0.943218158 + 0.972222222 x = 0.943218158 + 0.972222222 Combine like terms: 0.943218158 + 0.972222222 = 1.91544038 x = 1.91544038 Simplifying x = 1.91544038Subproblem 2
x + -0.972222222 = -0.943218158 Simplifying x + -0.972222222 = -0.943218158 Reorder the terms: -0.972222222 + x = -0.943218158 Solving -0.972222222 + x = -0.943218158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.972222222' to each side of the equation. -0.972222222 + 0.972222222 + x = -0.943218158 + 0.972222222 Combine like terms: -0.972222222 + 0.972222222 = 0.000000000 0.000000000 + x = -0.943218158 + 0.972222222 x = -0.943218158 + 0.972222222 Combine like terms: -0.943218158 + 0.972222222 = 0.029004064 x = 0.029004064 Simplifying x = 0.029004064Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.91544038, 0.029004064}
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