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Simplifying -66x2 + 2x + 1 = 0 Reorder the terms: 1 + 2x + -66x2 = 0 Solving 1 + 2x + -66x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -66 the coefficient of the squared term: Divide each side by '-66'. -0.01515151515 + -0.0303030303x + x2 = 0 Move the constant term to the right: Add '0.01515151515' to each side of the equation. -0.01515151515 + -0.0303030303x + 0.01515151515 + x2 = 0 + 0.01515151515 Reorder the terms: -0.01515151515 + 0.01515151515 + -0.0303030303x + x2 = 0 + 0.01515151515 Combine like terms: -0.01515151515 + 0.01515151515 = 0.00000000000 0.00000000000 + -0.0303030303x + x2 = 0 + 0.01515151515 -0.0303030303x + x2 = 0 + 0.01515151515 Combine like terms: 0 + 0.01515151515 = 0.01515151515 -0.0303030303x + x2 = 0.01515151515 The x term is -0.0303030303x. Take half its coefficient (-0.01515151515). Square it (0.0002295684113) and add it to both sides. Add '0.0002295684113' to each side of the equation. -0.0303030303x + 0.0002295684113 + x2 = 0.01515151515 + 0.0002295684113 Reorder the terms: 0.0002295684113 + -0.0303030303x + x2 = 0.01515151515 + 0.0002295684113 Combine like terms: 0.01515151515 + 0.0002295684113 = 0.0153810835613 0.0002295684113 + -0.0303030303x + x2 = 0.0153810835613 Factor a perfect square on the left side: (x + -0.01515151515)(x + -0.01515151515) = 0.0153810835613 Calculate the square root of the right side: 0.124020497 Break this problem into two subproblems by setting (x + -0.01515151515) equal to 0.124020497 and -0.124020497.Subproblem 1
x + -0.01515151515 = 0.124020497 Simplifying x + -0.01515151515 = 0.124020497 Reorder the terms: -0.01515151515 + x = 0.124020497 Solving -0.01515151515 + x = 0.124020497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01515151515' to each side of the equation. -0.01515151515 + 0.01515151515 + x = 0.124020497 + 0.01515151515 Combine like terms: -0.01515151515 + 0.01515151515 = 0.00000000000 0.00000000000 + x = 0.124020497 + 0.01515151515 x = 0.124020497 + 0.01515151515 Combine like terms: 0.124020497 + 0.01515151515 = 0.13917201215 x = 0.13917201215 Simplifying x = 0.13917201215Subproblem 2
x + -0.01515151515 = -0.124020497 Simplifying x + -0.01515151515 = -0.124020497 Reorder the terms: -0.01515151515 + x = -0.124020497 Solving -0.01515151515 + x = -0.124020497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01515151515' to each side of the equation. -0.01515151515 + 0.01515151515 + x = -0.124020497 + 0.01515151515 Combine like terms: -0.01515151515 + 0.01515151515 = 0.00000000000 0.00000000000 + x = -0.124020497 + 0.01515151515 x = -0.124020497 + 0.01515151515 Combine like terms: -0.124020497 + 0.01515151515 = -0.10886898185 x = -0.10886898185 Simplifying x = -0.10886898185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13917201215, -0.10886898185}
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