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Simplifying a2 + -34a + 102 = 0 Reorder the terms: 102 + -34a + a2 = 0 Solving 102 + -34a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-102' to each side of the equation. 102 + -34a + -102 + a2 = 0 + -102 Reorder the terms: 102 + -102 + -34a + a2 = 0 + -102 Combine like terms: 102 + -102 = 0 0 + -34a + a2 = 0 + -102 -34a + a2 = 0 + -102 Combine like terms: 0 + -102 = -102 -34a + a2 = -102 The a term is -34a. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34a + 289 + a2 = -102 + 289 Reorder the terms: 289 + -34a + a2 = -102 + 289 Combine like terms: -102 + 289 = 187 289 + -34a + a2 = 187 Factor a perfect square on the left side: (a + -17)(a + -17) = 187 Calculate the square root of the right side: 13.674794331 Break this problem into two subproblems by setting (a + -17) equal to 13.674794331 and -13.674794331.Subproblem 1
a + -17 = 13.674794331 Simplifying a + -17 = 13.674794331 Reorder the terms: -17 + a = 13.674794331 Solving -17 + a = 13.674794331 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + a = 13.674794331 + 17 Combine like terms: -17 + 17 = 0 0 + a = 13.674794331 + 17 a = 13.674794331 + 17 Combine like terms: 13.674794331 + 17 = 30.674794331 a = 30.674794331 Simplifying a = 30.674794331Subproblem 2
a + -17 = -13.674794331 Simplifying a + -17 = -13.674794331 Reorder the terms: -17 + a = -13.674794331 Solving -17 + a = -13.674794331 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + a = -13.674794331 + 17 Combine like terms: -17 + 17 = 0 0 + a = -13.674794331 + 17 a = -13.674794331 + 17 Combine like terms: -13.674794331 + 17 = 3.325205669 a = 3.325205669 Simplifying a = 3.325205669Solution
The solution to the problem is based on the solutions from the subproblems. a = {30.674794331, 3.325205669}
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