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Simplifying 80x2 + 80x + 11 = 0 Reorder the terms: 11 + 80x + 80x2 = 0 Solving 11 + 80x + 80x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. 0.1375 + x + x2 = 0 Move the constant term to the right: Add '-0.1375' to each side of the equation. 0.1375 + x + -0.1375 + x2 = 0 + -0.1375 Reorder the terms: 0.1375 + -0.1375 + x + x2 = 0 + -0.1375 Combine like terms: 0.1375 + -0.1375 = 0.0000 0.0000 + x + x2 = 0 + -0.1375 x + x2 = 0 + -0.1375 Combine like terms: 0 + -0.1375 = -0.1375 x + x2 = -0.1375 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. + 0.25 + x2 = -0.1375 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.1375 + 0.25 Combine like terms: -0.1375 + 0.25 = 0.1125 1.25 + x2 = 0.1125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1125 Calculate the square root of the right side: 0.335410197 Break this problem into two subproblems by setting (x + 0.5) equal to 0.335410197 and -0.335410197.Subproblem 1
x + 0.5 = 0.335410197 Simplifying x + 0.5 = 0.335410197 Reorder the terms: 0.5 + x = 0.335410197 Solving 0.5 + x = 0.335410197 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 = 0.335410197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.335410197 + -0.5 x = 0.335410197 + -0.5 Combine like terms: 0.335410197 + -0.5 = -0.164589803 x = -0.164589803 Simplifying x = -0.164589803Subproblem 2
x + 0.5 = -0.335410197 Simplifying x + 0.5 = -0.335410197 Reorder the terms: 0.5 + x = -0.335410197 Solving 0.5 + x = -0.335410197 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 = -0.335410197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.335410197 + -0.5 x = -0.335410197 + -0.5 Combine like terms: -0.335410197 + -0.5 = -0.835410197 x = -0.835410197 Simplifying x = -0.835410197Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.164589803, -0.835410197}
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