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Simplifying a = a(a + -21) + -100 Reorder the terms: a = a(-21 + a) + -100 a = (-21 * a + a * a) + -100 a = (-21a + a2) + -100 Reorder the terms: a = -100 + -21a + a2 Solving a = -100 + -21a + a2 Solving for variable 'a'. Reorder the terms: 100 + a + 21a + -1a2 = -100 + -21a + a2 + 100 + 21a + -1a2 Combine like terms: a + 21a = 22a 100 + 22a + -1a2 = -100 + -21a + a2 + 100 + 21a + -1a2 Reorder the terms: 100 + 22a + -1a2 = -100 + 100 + -21a + 21a + a2 + -1a2 Combine like terms: -100 + 100 = 0 100 + 22a + -1a2 = 0 + -21a + 21a + a2 + -1a2 100 + 22a + -1a2 = -21a + 21a + a2 + -1a2 Combine like terms: -21a + 21a = 0 100 + 22a + -1a2 = 0 + a2 + -1a2 100 + 22a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 100 + 22a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + -22a + a2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -22a + 100 + a2 = 0 + 100 Reorder the terms: -100 + 100 + -22a + a2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -22a + a2 = 0 + 100 -22a + a2 = 0 + 100 Combine like terms: 0 + 100 = 100 -22a + a2 = 100 The a term is -22a. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22a + 121 + a2 = 100 + 121 Reorder the terms: 121 + -22a + a2 = 100 + 121 Combine like terms: 100 + 121 = 221 121 + -22a + a2 = 221 Factor a perfect square on the left side: (a + -11)(a + -11) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (a + -11) equal to 14.866068747 and -14.866068747.Subproblem 1
a + -11 = 14.866068747 Simplifying a + -11 = 14.866068747 Reorder the terms: -11 + a = 14.866068747 Solving -11 + a = 14.866068747 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + a = 14.866068747 + 11 Combine like terms: -11 + 11 = 0 0 + a = 14.866068747 + 11 a = 14.866068747 + 11 Combine like terms: 14.866068747 + 11 = 25.866068747 a = 25.866068747 Simplifying a = 25.866068747Subproblem 2
a + -11 = -14.866068747 Simplifying a + -11 = -14.866068747 Reorder the terms: -11 + a = -14.866068747 Solving -11 + a = -14.866068747 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + a = -14.866068747 + 11 Combine like terms: -11 + 11 = 0 0 + a = -14.866068747 + 11 a = -14.866068747 + 11 Combine like terms: -14.866068747 + 11 = -3.866068747 a = -3.866068747 Simplifying a = -3.866068747Solution
The solution to the problem is based on the solutions from the subproblems. a = {25.866068747, -3.866068747}
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