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Simplifying (a + 3)(a + -3) = 2a Reorder the terms: (3 + a)(a + -3) = 2a Reorder the terms: (3 + a)(-3 + a) = 2a Multiply (3 + a) * (-3 + a) (3(-3 + a) + a(-3 + a)) = 2a ((-3 * 3 + a * 3) + a(-3 + a)) = 2a ((-9 + 3a) + a(-3 + a)) = 2a (-9 + 3a + (-3 * a + a * a)) = 2a (-9 + 3a + (-3a + a2)) = 2a Combine like terms: 3a + -3a = 0 (-9 + 0 + a2) = 2a (-9 + a2) = 2a Solving -9 + a2 = 2a Solving for variable 'a'. Reorder the terms: -9 + -2a + a2 = 2a + -2a Combine like terms: 2a + -2a = 0 -9 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -2a + 9 + a2 = 0 + 9 Reorder the terms: -9 + 9 + -2a + a2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2a + a2 = 0 + 9 -2a + a2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2a + a2 = 9 The a term is -2a. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2a + 1 + a2 = 9 + 1 Reorder the terms: 1 + -2a + a2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + -2a + a2 = 10 Factor a perfect square on the left side: (a + -1)(a + -1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (a + -1) equal to 3.16227766 and -3.16227766.Subproblem 1
a + -1 = 3.16227766 Simplifying a + -1 = 3.16227766 Reorder the terms: -1 + a = 3.16227766 Solving -1 + a = 3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = 3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + a = 3.16227766 + 1 a = 3.16227766 + 1 Combine like terms: 3.16227766 + 1 = 4.16227766 a = 4.16227766 Simplifying a = 4.16227766Subproblem 2
a + -1 = -3.16227766 Simplifying a + -1 = -3.16227766 Reorder the terms: -1 + a = -3.16227766 Solving -1 + a = -3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + a = -3.16227766 + 1 Combine like terms: -1 + 1 = 0 0 + a = -3.16227766 + 1 a = -3.16227766 + 1 Combine like terms: -3.16227766 + 1 = -2.16227766 a = -2.16227766 Simplifying a = -2.16227766Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.16227766, -2.16227766}
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