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Simplifying 55.5x2 + x + -55 = 0 Reorder the terms: -55 + x + 55.5x2 = 0 Solving -55 + x + 55.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 55.5 the coefficient of the squared term: Divide each side by '55.5'. -0.990990991 + 0.01801801802x + x2 = 0 Move the constant term to the right: Add '0.990990991' to each side of the equation. -0.990990991 + 0.01801801802x + 0.990990991 + x2 = 0 + 0.990990991 Reorder the terms: -0.990990991 + 0.990990991 + 0.01801801802x + x2 = 0 + 0.990990991 Combine like terms: -0.990990991 + 0.990990991 = 0.000000000 0.000000000 + 0.01801801802x + x2 = 0 + 0.990990991 0.01801801802x + x2 = 0 + 0.990990991 Combine like terms: 0 + 0.990990991 = 0.990990991 0.01801801802x + x2 = 0.990990991 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. 0.01801801802x + 0.25 + x2 = 0.990990991 + 0.25 Reorder the terms: 0.25 + 0.01801801802x + x2 = 0.990990991 + 0.25 Combine like terms: 0.990990991 + 0.25 = 1.240990991 0.25 + 0.01801801802x + x2 = 1.240990991 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.240990991 Calculate the square root of the right side: 1.113997752 Break this problem into two subproblems by setting (x + 0.5) equal to 1.113997752 and -1.113997752.Subproblem 1
x + 0.5 = 1.113997752 Simplifying x + 0.5 = 1.113997752 Reorder the terms: 0.5 + x = 1.113997752 Solving 0.5 + x = 1.113997752 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 = 1.113997752 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.113997752 + -0.5 x = 1.113997752 + -0.5 Combine like terms: 1.113997752 + -0.5 = 0.613997752 x = 0.613997752 Simplifying x = 0.613997752Subproblem 2
x + 0.5 = -1.113997752 Simplifying x + 0.5 = -1.113997752 Reorder the terms: 0.5 + x = -1.113997752 Solving 0.5 + x = -1.113997752 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 = -1.113997752 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.113997752 + -0.5 x = -1.113997752 + -0.5 Combine like terms: -1.113997752 + -0.5 = -1.613997752 x = -1.613997752 Simplifying x = -1.613997752Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.613997752, -1.613997752}
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