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Simplifying a2 + -12a + 15 = 0 Reorder the terms: 15 + -12a + a2 = 0 Solving 15 + -12a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -12a + -15 + a2 = 0 + -15 Reorder the terms: 15 + -15 + -12a + a2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -12a + a2 = 0 + -15 -12a + a2 = 0 + -15 Combine like terms: 0 + -15 = -15 -12a + a2 = -15 The a term is -12a. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12a + 36 + a2 = -15 + 36 Reorder the terms: 36 + -12a + a2 = -15 + 36 Combine like terms: -15 + 36 = 21 36 + -12a + a2 = 21 Factor a perfect square on the left side: (a + -6)(a + -6) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (a + -6) equal to 4.582575695 and -4.582575695.Subproblem 1
a + -6 = 4.582575695 Simplifying a + -6 = 4.582575695 Reorder the terms: -6 + a = 4.582575695 Solving -6 + a = 4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = 4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + a = 4.582575695 + 6 a = 4.582575695 + 6 Combine like terms: 4.582575695 + 6 = 10.582575695 a = 10.582575695 Simplifying a = 10.582575695Subproblem 2
a + -6 = -4.582575695 Simplifying a + -6 = -4.582575695 Reorder the terms: -6 + a = -4.582575695 Solving -6 + a = -4.582575695 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + a = -4.582575695 + 6 Combine like terms: -6 + 6 = 0 0 + a = -4.582575695 + 6 a = -4.582575695 + 6 Combine like terms: -4.582575695 + 6 = 1.417424305 a = 1.417424305 Simplifying a = 1.417424305Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.582575695, 1.417424305}
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