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Simplifying a2 + 10a + -65 = 4 Reorder the terms: -65 + 10a + a2 = 4 Solving -65 + 10a + a2 = 4 Solving for variable 'a'. Reorder the terms: -65 + -4 + 10a + a2 = 4 + -4 Combine like terms: -65 + -4 = -69 -69 + 10a + a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -69 + 10a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '69' to each side of the equation. -69 + 10a + 69 + a2 = 0 + 69 Reorder the terms: -69 + 69 + 10a + a2 = 0 + 69 Combine like terms: -69 + 69 = 0 0 + 10a + a2 = 0 + 69 10a + a2 = 0 + 69 Combine like terms: 0 + 69 = 69 10a + a2 = 69 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 = 69 + 25 Reorder the terms: 25 + 10a + a2 = 69 + 25 Combine like terms: 69 + 25 = 94 25 + 10a + a2 = 94 Factor a perfect square on the left side: (a + 5)(a + 5) = 94 Calculate the square root of the right side: 9.695359715 Break this problem into two subproblems by setting (a + 5) equal to 9.695359715 and -9.695359715.Subproblem 1
a + 5 = 9.695359715 Simplifying a + 5 = 9.695359715 Reorder the terms: 5 + a = 9.695359715 Solving 5 + a = 9.695359715 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 = 9.695359715 + -5 Combine like terms: 5 + -5 = 0 0 + a = 9.695359715 + -5 a = 9.695359715 + -5 Combine like terms: 9.695359715 + -5 = 4.695359715 a = 4.695359715 Simplifying a = 4.695359715Subproblem 2
a + 5 = -9.695359715 Simplifying a + 5 = -9.695359715 Reorder the terms: 5 + a = -9.695359715 Solving 5 + a = -9.695359715 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 = -9.695359715 + -5 Combine like terms: 5 + -5 = 0 0 + a = -9.695359715 + -5 a = -9.695359715 + -5 Combine like terms: -9.695359715 + -5 = -14.695359715 a = -14.695359715 Simplifying a = -14.695359715Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.695359715, -14.695359715}
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