a^2=9a+14

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Solution for a^2=9a+14 equation:


Simplifying
a2 = 9a + 14

Reorder the terms:
a2 = 14 + 9a

Solving
a2 = 14 + 9a

Solving for variable 'a'.

Reorder the terms:
-14 + -9a + a2 = 14 + 9a + -14 + -9a

Reorder the terms:
-14 + -9a + a2 = 14 + -14 + 9a + -9a

Combine like terms: 14 + -14 = 0
-14 + -9a + a2 = 0 + 9a + -9a
-14 + -9a + a2 = 9a + -9a

Combine like terms: 9a + -9a = 0
-14 + -9a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -9a + 14 + a2 = 0 + 14

Reorder the terms:
-14 + 14 + -9a + a2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -9a + a2 = 0 + 14
-9a + a2 = 0 + 14

Combine like terms: 0 + 14 = 14
-9a + a2 = 14

The a term is -9a.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9a + 20.25 + a2 = 14 + 20.25

Reorder the terms:
20.25 + -9a + a2 = 14 + 20.25

Combine like terms: 14 + 20.25 = 34.25
20.25 + -9a + a2 = 34.25

Factor a perfect square on the left side:
(a + -4.5)(a + -4.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(a + -4.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

a + -4.5 = 5.852349955 Simplifying a + -4.5 = 5.852349955 Reorder the terms: -4.5 + a = 5.852349955 Solving -4.5 + a = 5.852349955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = 5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = 5.852349955 + 4.5 a = 5.852349955 + 4.5 Combine like terms: 5.852349955 + 4.5 = 10.352349955 a = 10.352349955 Simplifying a = 10.352349955

Subproblem 2

a + -4.5 = -5.852349955 Simplifying a + -4.5 = -5.852349955 Reorder the terms: -4.5 + a = -5.852349955 Solving -4.5 + a = -5.852349955 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + a = -5.852349955 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + a = -5.852349955 + 4.5 a = -5.852349955 + 4.5 Combine like terms: -5.852349955 + 4.5 = -1.352349955 a = -1.352349955 Simplifying a = -1.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. a = {10.352349955, -1.352349955}

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