a^2-6a+11=92

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Solution for a^2-6a+11=92 equation:


Simplifying
a2 + -6a + 11 = 92

Reorder the terms:
11 + -6a + a2 = 92

Solving
11 + -6a + a2 = 92

Solving for variable 'a'.

Reorder the terms:
11 + -92 + -6a + a2 = 92 + -92

Combine like terms: 11 + -92 = -81
-81 + -6a + a2 = 92 + -92

Combine like terms: 92 + -92 = 0
-81 + -6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -6a + 81 + a2 = 0 + 81

Reorder the terms:
-81 + 81 + -6a + a2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -6a + a2 = 0 + 81
-6a + a2 = 0 + 81

Combine like terms: 0 + 81 = 81
-6a + a2 = 81

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = 81 + 9

Reorder the terms:
9 + -6a + a2 = 81 + 9

Combine like terms: 81 + 9 = 90
9 + -6a + a2 = 90

Factor a perfect square on the left side:
(a + -3)(a + -3) = 90

Calculate the square root of the right side: 9.486832981

Break this problem into two subproblems by setting 
(a + -3) equal to 9.486832981 and -9.486832981.

Subproblem 1

a + -3 = 9.486832981 Simplifying a + -3 = 9.486832981 Reorder the terms: -3 + a = 9.486832981 Solving -3 + a = 9.486832981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 9.486832981 + 3 Combine like terms: -3 + 3 = 0 0 + a = 9.486832981 + 3 a = 9.486832981 + 3 Combine like terms: 9.486832981 + 3 = 12.486832981 a = 12.486832981 Simplifying a = 12.486832981

Subproblem 2

a + -3 = -9.486832981 Simplifying a + -3 = -9.486832981 Reorder the terms: -3 + a = -9.486832981 Solving -3 + a = -9.486832981 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -9.486832981 + 3 Combine like terms: -3 + 3 = 0 0 + a = -9.486832981 + 3 a = -9.486832981 + 3 Combine like terms: -9.486832981 + 3 = -6.486832981 a = -6.486832981 Simplifying a = -6.486832981

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.486832981, -6.486832981}

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