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Simplifying a2 + -4a + -10 = -2 Reorder the terms: -10 + -4a + a2 = -2 Solving -10 + -4a + a2 = -2 Solving for variable 'a'. Reorder the terms: -10 + 2 + -4a + a2 = -2 + 2 Combine like terms: -10 + 2 = -8 -8 + -4a + a2 = -2 + 2 Combine like terms: -2 + 2 = 0 -8 + -4a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4a + 8 + a2 = 0 + 8 Reorder the terms: -8 + 8 + -4a + a2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4a + a2 = 0 + 8 -4a + a2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4a + a2 = 8 The a term is -4a. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4a + 4 + a2 = 8 + 4 Reorder the terms: 4 + -4a + a2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4a + a2 = 12 Factor a perfect square on the left side: (a + -2)(a + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (a + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
a + -2 = 3.464101615 Simplifying a + -2 = 3.464101615 Reorder the terms: -2 + a = 3.464101615 Solving -2 + a = 3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + a = 3.464101615 + 2 a = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 a = 5.464101615 Simplifying a = 5.464101615Subproblem 2
a + -2 = -3.464101615 Simplifying a + -2 = -3.464101615 Reorder the terms: -2 + a = -3.464101615 Solving -2 + a = -3.464101615 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + a = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + a = -3.464101615 + 2 a = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 a = -1.464101615 Simplifying a = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. a = {5.464101615, -1.464101615}
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