a^2=11a+24

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


Simplifying
a2 = 11a + 24

Reorder the terms:
a2 = 24 + 11a

Solving
a2 = 24 + 11a

Solving for variable 'a'.

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

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

Combine like terms: 24 + -24 = 0
-24 + -11a + a2 = 0 + 11a + -11a
-24 + -11a + a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
-24 + -11a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -11a + 24 + a2 = 0 + 24

Reorder the terms:
-24 + 24 + -11a + a2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -11a + a2 = 0 + 24
-11a + a2 = 0 + 24

Combine like terms: 0 + 24 = 24
-11a + a2 = 24

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 = 24 + 30.25

Reorder the terms:
30.25 + -11a + a2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + -11a + a2 = 54.25

Factor a perfect square on the left side:
(a + -5.5)(a + -5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(a + -5.5) equal to 7.365459931 and -7.365459931.

Subproblem 1

a + -5.5 = 7.365459931 Simplifying a + -5.5 = 7.365459931 Reorder the terms: -5.5 + a = 7.365459931 Solving -5.5 + a = 7.365459931 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 = 7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 7.365459931 + 5.5 a = 7.365459931 + 5.5 Combine like terms: 7.365459931 + 5.5 = 12.865459931 a = 12.865459931 Simplifying a = 12.865459931

Subproblem 2

a + -5.5 = -7.365459931 Simplifying a + -5.5 = -7.365459931 Reorder the terms: -5.5 + a = -7.365459931 Solving -5.5 + a = -7.365459931 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 = -7.365459931 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -7.365459931 + 5.5 a = -7.365459931 + 5.5 Combine like terms: -7.365459931 + 5.5 = -1.865459931 a = -1.865459931 Simplifying a = -1.865459931

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.865459931, -1.865459931}

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