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Simplifying a2 + -24a + -95 = 0 Reorder the terms: -95 + -24a + a2 = 0 Solving -95 + -24a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + -24a + 95 + a2 = 0 + 95 Reorder the terms: -95 + 95 + -24a + a2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -24a + a2 = 0 + 95 -24a + a2 = 0 + 95 Combine like terms: 0 + 95 = 95 -24a + a2 = 95 The a term is -24a. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24a + 144 + a2 = 95 + 144 Reorder the terms: 144 + -24a + a2 = 95 + 144 Combine like terms: 95 + 144 = 239 144 + -24a + a2 = 239 Factor a perfect square on the left side: (a + -12)(a + -12) = 239 Calculate the square root of the right side: 15.459624834 Break this problem into two subproblems by setting (a + -12) equal to 15.459624834 and -15.459624834.Subproblem 1
a + -12 = 15.459624834 Simplifying a + -12 = 15.459624834 Reorder the terms: -12 + a = 15.459624834 Solving -12 + a = 15.459624834 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = 15.459624834 + 12 Combine like terms: -12 + 12 = 0 0 + a = 15.459624834 + 12 a = 15.459624834 + 12 Combine like terms: 15.459624834 + 12 = 27.459624834 a = 27.459624834 Simplifying a = 27.459624834Subproblem 2
a + -12 = -15.459624834 Simplifying a + -12 = -15.459624834 Reorder the terms: -12 + a = -15.459624834 Solving -12 + a = -15.459624834 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + a = -15.459624834 + 12 Combine like terms: -12 + 12 = 0 0 + a = -15.459624834 + 12 a = -15.459624834 + 12 Combine like terms: -15.459624834 + 12 = -3.459624834 a = -3.459624834 Simplifying a = -3.459624834Solution
The solution to the problem is based on the solutions from the subproblems. a = {27.459624834, -3.459624834}
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