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Simplifying a2 + 10a + -216 = 0 Reorder the terms: -216 + 10a + a2 = 0 Solving -216 + 10a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '216' to each side of the equation. -216 + 10a + 216 + a2 = 0 + 216 Reorder the terms: -216 + 216 + 10a + a2 = 0 + 216 Combine like terms: -216 + 216 = 0 0 + 10a + a2 = 0 + 216 10a + a2 = 0 + 216 Combine like terms: 0 + 216 = 216 10a + a2 = 216 The a term is 10a. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10a + 25 + a2 = 216 + 25 Reorder the terms: 25 + 10a + a2 = 216 + 25 Combine like terms: 216 + 25 = 241 25 + 10a + a2 = 241 Factor a perfect square on the left side: (a + 5)(a + 5) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (a + 5) equal to 15.524174696 and -15.524174696.Subproblem 1
a + 5 = 15.524174696 Simplifying a + 5 = 15.524174696 Reorder the terms: 5 + a = 15.524174696 Solving 5 + a = 15.524174696 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 15.524174696 + -5 Combine like terms: 5 + -5 = 0 0 + a = 15.524174696 + -5 a = 15.524174696 + -5 Combine like terms: 15.524174696 + -5 = 10.524174696 a = 10.524174696 Simplifying a = 10.524174696Subproblem 2
a + 5 = -15.524174696 Simplifying a + 5 = -15.524174696 Reorder the terms: 5 + a = -15.524174696 Solving 5 + a = -15.524174696 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -15.524174696 + -5 Combine like terms: 5 + -5 = 0 0 + a = -15.524174696 + -5 a = -15.524174696 + -5 Combine like terms: -15.524174696 + -5 = -20.524174696 a = -20.524174696 Simplifying a = -20.524174696Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.524174696, -20.524174696}
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