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Simplifying 18x2 + x + -35 = 0 Reorder the terms: -35 + x + 18x2 = 0 Solving -35 + x + 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'. -1.944444444 + 0.05555555556x + x2 = 0 Move the constant term to the right: Add '1.944444444' to each side of the equation. -1.944444444 + 0.05555555556x + 1.944444444 + x2 = 0 + 1.944444444 Reorder the terms: -1.944444444 + 1.944444444 + 0.05555555556x + x2 = 0 + 1.944444444 Combine like terms: -1.944444444 + 1.944444444 = 0.000000000 0.000000000 + 0.05555555556x + x2 = 0 + 1.944444444 0.05555555556x + x2 = 0 + 1.944444444 Combine like terms: 0 + 1.944444444 = 1.944444444 0.05555555556x + x2 = 1.944444444 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 = 1.944444444 + 0.25 Reorder the terms: 0.25 + 0.05555555556x + x2 = 1.944444444 + 0.25 Combine like terms: 1.944444444 + 0.25 = 2.194444444 0.25 + 0.05555555556x + x2 = 2.194444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.194444444 Calculate the square root of the right side: 1.481365736 Break this problem into two subproblems by setting (x + 0.5) equal to 1.481365736 and -1.481365736.Subproblem 1
x + 0.5 = 1.481365736 Simplifying x + 0.5 = 1.481365736 Reorder the terms: 0.5 + x = 1.481365736 Solving 0.5 + x = 1.481365736 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 = 1.481365736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.481365736 + -0.5 x = 1.481365736 + -0.5 Combine like terms: 1.481365736 + -0.5 = 0.981365736 x = 0.981365736 Simplifying x = 0.981365736Subproblem 2
x + 0.5 = -1.481365736 Simplifying x + 0.5 = -1.481365736 Reorder the terms: 0.5 + x = -1.481365736 Solving 0.5 + x = -1.481365736 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 = -1.481365736 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.481365736 + -0.5 x = -1.481365736 + -0.5 Combine like terms: -1.481365736 + -0.5 = -1.981365736 x = -1.981365736 Simplifying x = -1.981365736Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.981365736, -1.981365736}
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