a^2-11a+24=04

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Solution for a^2-11a+24=04 equation:


Simplifying
a2 + -11a + 24 = 4

Reorder the terms:
24 + -11a + a2 = 4

Solving
24 + -11a + a2 = 4

Solving for variable 'a'.

Reorder the terms:
24 + -4 + -11a + a2 = 4 + -4

Combine like terms: 24 + -4 = 20
20 + -11a + a2 = 4 + -4

Combine like terms: 4 + -4 = 0
20 + -11a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -11a + -20 + a2 = 0 + -20

Reorder the terms:
20 + -20 + -11a + a2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -11a + a2 = 0 + -20
-11a + a2 = 0 + -20

Combine like terms: 0 + -20 = -20
-11a + a2 = -20

The a term is -11a.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11a + 30.25 + a2 = -20 + 30.25

Reorder the terms:
30.25 + -11a + a2 = -20 + 30.25

Combine like terms: -20 + 30.25 = 10.25
30.25 + -11a + a2 = 10.25

Factor a perfect square on the left side:
(a + -5.5)(a + -5.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(a + -5.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

a + -5.5 = 3.201562119 Simplifying a + -5.5 = 3.201562119 Reorder the terms: -5.5 + a = 3.201562119 Solving -5.5 + a = 3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 3.201562119 + 5.5 a = 3.201562119 + 5.5 Combine like terms: 3.201562119 + 5.5 = 8.701562119 a = 8.701562119 Simplifying a = 8.701562119

Subproblem 2

a + -5.5 = -3.201562119 Simplifying a + -5.5 = -3.201562119 Reorder the terms: -5.5 + a = -3.201562119 Solving -5.5 + a = -3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -3.201562119 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -3.201562119 + 5.5 a = -3.201562119 + 5.5 Combine like terms: -3.201562119 + 5.5 = 2.298437881 a = 2.298437881 Simplifying a = 2.298437881

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.701562119, 2.298437881}

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