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Simplifying a2 + -8a = 15 Reorder the terms: -8a + a2 = 15 Solving -8a + a2 = 15 Solving for variable 'a'. Reorder the terms: -15 + -8a + a2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -8a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -8a + 15 + a2 = 0 + 15 Reorder the terms: -15 + 15 + -8a + a2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -8a + a2 = 0 + 15 -8a + a2 = 0 + 15 Combine like terms: 0 + 15 = 15 -8a + a2 = 15 The a term is -8a. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8a + 16 + a2 = 15 + 16 Reorder the terms: 16 + -8a + a2 = 15 + 16 Combine like terms: 15 + 16 = 31 16 + -8a + a2 = 31 Factor a perfect square on the left side: (a + -4)(a + -4) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (a + -4) equal to 5.567764363 and -5.567764363.Subproblem 1
a + -4 = 5.567764363 Simplifying a + -4 = 5.567764363 Reorder the terms: -4 + a = 5.567764363 Solving -4 + a = 5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = 5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + a = 5.567764363 + 4 a = 5.567764363 + 4 Combine like terms: 5.567764363 + 4 = 9.567764363 a = 9.567764363 Simplifying a = 9.567764363Subproblem 2
a + -4 = -5.567764363 Simplifying a + -4 = -5.567764363 Reorder the terms: -4 + a = -5.567764363 Solving -4 + a = -5.567764363 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + a = -5.567764363 + 4 Combine like terms: -4 + 4 = 0 0 + a = -5.567764363 + 4 a = -5.567764363 + 4 Combine like terms: -5.567764363 + 4 = -1.567764363 a = -1.567764363 Simplifying a = -1.567764363Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.567764363, -1.567764363}
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