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Simplifying (a + 16)(a + -18) = 180 Reorder the terms: (16 + a)(a + -18) = 180 Reorder the terms: (16 + a)(-18 + a) = 180 Multiply (16 + a) * (-18 + a) (16(-18 + a) + a(-18 + a)) = 180 ((-18 * 16 + a * 16) + a(-18 + a)) = 180 ((-288 + 16a) + a(-18 + a)) = 180 (-288 + 16a + (-18 * a + a * a)) = 180 (-288 + 16a + (-18a + a2)) = 180 Combine like terms: 16a + -18a = -2a (-288 + -2a + a2) = 180 Solving -288 + -2a + a2 = 180 Solving for variable 'a'. Reorder the terms: -288 + -180 + -2a + a2 = 180 + -180 Combine like terms: -288 + -180 = -468 -468 + -2a + a2 = 180 + -180 Combine like terms: 180 + -180 = 0 -468 + -2a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '468' to each side of the equation. -468 + -2a + 468 + a2 = 0 + 468 Reorder the terms: -468 + 468 + -2a + a2 = 0 + 468 Combine like terms: -468 + 468 = 0 0 + -2a + a2 = 0 + 468 -2a + a2 = 0 + 468 Combine like terms: 0 + 468 = 468 -2a + a2 = 468 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 = 468 + 1 Reorder the terms: 1 + -2a + a2 = 468 + 1 Combine like terms: 468 + 1 = 469 1 + -2a + a2 = 469 Factor a perfect square on the left side: (a + -1)(a + -1) = 469 Calculate the square root of the right side: 21.656407828 Break this problem into two subproblems by setting (a + -1) equal to 21.656407828 and -21.656407828.Subproblem 1
a + -1 = 21.656407828 Simplifying a + -1 = 21.656407828 Reorder the terms: -1 + a = 21.656407828 Solving -1 + a = 21.656407828 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 = 21.656407828 + 1 Combine like terms: -1 + 1 = 0 0 + a = 21.656407828 + 1 a = 21.656407828 + 1 Combine like terms: 21.656407828 + 1 = 22.656407828 a = 22.656407828 Simplifying a = 22.656407828Subproblem 2
a + -1 = -21.656407828 Simplifying a + -1 = -21.656407828 Reorder the terms: -1 + a = -21.656407828 Solving -1 + a = -21.656407828 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 = -21.656407828 + 1 Combine like terms: -1 + 1 = 0 0 + a = -21.656407828 + 1 a = -21.656407828 + 1 Combine like terms: -21.656407828 + 1 = -20.656407828 a = -20.656407828 Simplifying a = -20.656407828Solution
The solution to the problem is based on the solutions from the subproblems. a = {22.656407828, -20.656407828}
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