a^2+18a+81=90

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Solution for a^2+18a+81=90 equation:


Simplifying
a2 + 18a + 81 = 90

Reorder the terms:
81 + 18a + a2 = 90

Solving
81 + 18a + a2 = 90

Solving for variable 'a'.

Reorder the terms:
81 + -90 + 18a + a2 = 90 + -90

Combine like terms: 81 + -90 = -9
-9 + 18a + a2 = 90 + -90

Combine like terms: 90 + -90 = 0
-9 + 18a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 18a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 18a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 18a + a2 = 0 + 9
18a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
18a + a2 = 9

The a term is 18a.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18a + 81 + a2 = 9 + 81

Reorder the terms:
81 + 18a + a2 = 9 + 81

Combine like terms: 9 + 81 = 90
81 + 18a + a2 = 90

Factor a perfect square on the left side:
(a + 9)(a + 9) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(a + 9) equal to 9.486832981 and -9.486832981.

Subproblem 1

a + 9 = 9.486832981 Simplifying a + 9 = 9.486832981 Reorder the terms: 9 + a = 9.486832981 Solving 9 + a = 9.486832981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = 9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + a = 9.486832981 + -9 a = 9.486832981 + -9 Combine like terms: 9.486832981 + -9 = 0.486832981 a = 0.486832981 Simplifying a = 0.486832981

Subproblem 2

a + 9 = -9.486832981 Simplifying a + 9 = -9.486832981 Reorder the terms: 9 + a = -9.486832981 Solving 9 + a = -9.486832981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + a = -9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + a = -9.486832981 + -9 a = -9.486832981 + -9 Combine like terms: -9.486832981 + -9 = -18.486832981 a = -18.486832981 Simplifying a = -18.486832981

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.486832981, -18.486832981}

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