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Simplifying 2(a + 2) + 4(a) = a(a + 2) Reorder the terms: 2(2 + a) + 4(a) = a(a + 2) (2 * 2 + a * 2) + 4(a) = a(a + 2) (4 + 2a) + 4(a) = a(a + 2) Combine like terms: 2a + 4a = 6a 4 + 6a = a(a + 2) Reorder the terms: 4 + 6a = a(2 + a) 4 + 6a = (2 * a + a * a) 4 + 6a = (2a + a2) Solving 4 + 6a = 2a + a2 Solving for variable 'a'. Combine like terms: 6a + -2a = 4a 4 + 4a + -1a2 = 2a + a2 + -2a + -1a2 Reorder the terms: 4 + 4a + -1a2 = 2a + -2a + a2 + -1a2 Combine like terms: 2a + -2a = 0 4 + 4a + -1a2 = 0 + a2 + -1a2 4 + 4a + -1a2 = a2 + -1a2 Combine like terms: a2 + -1a2 = 0 4 + 4a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4a + a2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -4a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4a + a2 = 0 + 4 -4a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4a + a2 = 4 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 = 4 + 4 Reorder the terms: 4 + -4a + a2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4a + a2 = 8 Factor a perfect square on the left side: (a + -2)(a + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (a + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
a + -2 = 2.828427125 Simplifying a + -2 = 2.828427125 Reorder the terms: -2 + a = 2.828427125 Solving -2 + a = 2.828427125 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 = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + a = 2.828427125 + 2 a = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 a = 4.828427125 Simplifying a = 4.828427125Subproblem 2
a + -2 = -2.828427125 Simplifying a + -2 = -2.828427125 Reorder the terms: -2 + a = -2.828427125 Solving -2 + a = -2.828427125 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 = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + a = -2.828427125 + 2 a = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 a = -0.828427125 Simplifying a = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.828427125, -0.828427125}
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