(a+16)(a-18)=180

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Solution for (a+16)(a-18)=180 equation:


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 = 22.656407828

Subproblem 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 = -20.656407828

Solution

The solution to the problem is based on the solutions from the subproblems. a = {22.656407828, -20.656407828}

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