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Simplifying a2 + -22a + 42 = 0 Reorder the terms: 42 + -22a + a2 = 0 Solving 42 + -22a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -22a + -42 + a2 = 0 + -42 Reorder the terms: 42 + -42 + -22a + a2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -22a + a2 = 0 + -42 -22a + a2 = 0 + -42 Combine like terms: 0 + -42 = -42 -22a + a2 = -42 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 = -42 + 121 Reorder the terms: 121 + -22a + a2 = -42 + 121 Combine like terms: -42 + 121 = 79 121 + -22a + a2 = 79 Factor a perfect square on the left side: (a + -11)(a + -11) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (a + -11) equal to 8.888194417 and -8.888194417.Subproblem 1
a + -11 = 8.888194417 Simplifying a + -11 = 8.888194417 Reorder the terms: -11 + a = 8.888194417 Solving -11 + a = 8.888194417 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 = 8.888194417 + 11 Combine like terms: -11 + 11 = 0 0 + a = 8.888194417 + 11 a = 8.888194417 + 11 Combine like terms: 8.888194417 + 11 = 19.888194417 a = 19.888194417 Simplifying a = 19.888194417Subproblem 2
a + -11 = -8.888194417 Simplifying a + -11 = -8.888194417 Reorder the terms: -11 + a = -8.888194417 Solving -11 + a = -8.888194417 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 = -8.888194417 + 11 Combine like terms: -11 + 11 = 0 0 + a = -8.888194417 + 11 a = -8.888194417 + 11 Combine like terms: -8.888194417 + 11 = 2.111805583 a = 2.111805583 Simplifying a = 2.111805583Solution
The solution to the problem is based on the solutions from the subproblems. a = {19.888194417, 2.111805583}
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