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Simplifying a2 + 8a + -188 = 0 Reorder the terms: -188 + 8a + a2 = 0 Solving -188 + 8a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + 8a + 188 + a2 = 0 + 188 Reorder the terms: -188 + 188 + 8a + a2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + 8a + a2 = 0 + 188 8a + a2 = 0 + 188 Combine like terms: 0 + 188 = 188 8a + a2 = 188 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 = 188 + 16 Reorder the terms: 16 + 8a + a2 = 188 + 16 Combine like terms: 188 + 16 = 204 16 + 8a + a2 = 204 Factor a perfect square on the left side: (a + 4)(a + 4) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (a + 4) equal to 14.282856857 and -14.282856857.Subproblem 1
a + 4 = 14.282856857 Simplifying a + 4 = 14.282856857 Reorder the terms: 4 + a = 14.282856857 Solving 4 + a = 14.282856857 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 = 14.282856857 + -4 Combine like terms: 4 + -4 = 0 0 + a = 14.282856857 + -4 a = 14.282856857 + -4 Combine like terms: 14.282856857 + -4 = 10.282856857 a = 10.282856857 Simplifying a = 10.282856857Subproblem 2
a + 4 = -14.282856857 Simplifying a + 4 = -14.282856857 Reorder the terms: 4 + a = -14.282856857 Solving 4 + a = -14.282856857 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 = -14.282856857 + -4 Combine like terms: 4 + -4 = 0 0 + a = -14.282856857 + -4 a = -14.282856857 + -4 Combine like terms: -14.282856857 + -4 = -18.282856857 a = -18.282856857 Simplifying a = -18.282856857Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.282856857, -18.282856857}
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