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Simplifying a2 + 8a + -53 = 0 Reorder the terms: -53 + 8a + a2 = 0 Solving -53 + 8a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 8a + 53 + a2 = 0 + 53 Reorder the terms: -53 + 53 + 8a + a2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 8a + a2 = 0 + 53 8a + a2 = 0 + 53 Combine like terms: 0 + 53 = 53 8a + a2 = 53 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 = 53 + 16 Reorder the terms: 16 + 8a + a2 = 53 + 16 Combine like terms: 53 + 16 = 69 16 + 8a + a2 = 69 Factor a perfect square on the left side: (a + 4)(a + 4) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (a + 4) equal to 8.306623863 and -8.306623863.Subproblem 1
a + 4 = 8.306623863 Simplifying a + 4 = 8.306623863 Reorder the terms: 4 + a = 8.306623863 Solving 4 + a = 8.306623863 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 = 8.306623863 + -4 Combine like terms: 4 + -4 = 0 0 + a = 8.306623863 + -4 a = 8.306623863 + -4 Combine like terms: 8.306623863 + -4 = 4.306623863 a = 4.306623863 Simplifying a = 4.306623863Subproblem 2
a + 4 = -8.306623863 Simplifying a + 4 = -8.306623863 Reorder the terms: 4 + a = -8.306623863 Solving 4 + a = -8.306623863 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 = -8.306623863 + -4 Combine like terms: 4 + -4 = 0 0 + a = -8.306623863 + -4 a = -8.306623863 + -4 Combine like terms: -8.306623863 + -4 = -12.306623863 a = -12.306623863 Simplifying a = -12.306623863Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.306623863, -12.306623863}
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