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Simplifying 55a + -99a * a = 3 Multiply a * a 55a + -99a2 = 3 Solving 55a + -99a2 = 3 Solving for variable 'a'. Reorder the terms: -3 + 55a + -99a2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 55a + -99a2 = 0 Begin completing the square. Divide all terms by -99 the coefficient of the squared term: Divide each side by '-99'. 0.0303030303 + -0.5555555556a + a2 = 0 Move the constant term to the right: Add '-0.0303030303' to each side of the equation. 0.0303030303 + -0.5555555556a + -0.0303030303 + a2 = 0 + -0.0303030303 Reorder the terms: 0.0303030303 + -0.0303030303 + -0.5555555556a + a2 = 0 + -0.0303030303 Combine like terms: 0.0303030303 + -0.0303030303 = 0.0000000000 0.0000000000 + -0.5555555556a + a2 = 0 + -0.0303030303 -0.5555555556a + a2 = 0 + -0.0303030303 Combine like terms: 0 + -0.0303030303 = -0.0303030303 -0.5555555556a + a2 = -0.0303030303 The a term is -0.5555555556a. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556a + 0.07716049384 + a2 = -0.0303030303 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556a + a2 = -0.0303030303 + 0.07716049384 Combine like terms: -0.0303030303 + 0.07716049384 = 0.04685746354 0.07716049384 + -0.5555555556a + a2 = 0.04685746354 Factor a perfect square on the left side: (a + -0.2777777778)(a + -0.2777777778) = 0.04685746354 Calculate the square root of the right side: 0.216465848 Break this problem into two subproblems by setting (a + -0.2777777778) equal to 0.216465848 and -0.216465848.Subproblem 1
a + -0.2777777778 = 0.216465848 Simplifying a + -0.2777777778 = 0.216465848 Reorder the terms: -0.2777777778 + a = 0.216465848 Solving -0.2777777778 + a = 0.216465848 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = 0.216465848 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = 0.216465848 + 0.2777777778 a = 0.216465848 + 0.2777777778 Combine like terms: 0.216465848 + 0.2777777778 = 0.4942436258 a = 0.4942436258 Simplifying a = 0.4942436258Subproblem 2
a + -0.2777777778 = -0.216465848 Simplifying a + -0.2777777778 = -0.216465848 Reorder the terms: -0.2777777778 + a = -0.216465848 Solving -0.2777777778 + a = -0.216465848 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + a = -0.216465848 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + a = -0.216465848 + 0.2777777778 a = -0.216465848 + 0.2777777778 Combine like terms: -0.216465848 + 0.2777777778 = 0.0613119298 a = 0.0613119298 Simplifying a = 0.0613119298Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.4942436258, 0.0613119298}
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