a^2-3a=3a+25

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Solution for a^2-3a=3a+25 equation:


Simplifying
a2 + -3a = 3a + 25

Reorder the terms:
-3a + a2 = 3a + 25

Reorder the terms:
-3a + a2 = 25 + 3a

Solving
-3a + a2 = 25 + 3a

Solving for variable 'a'.

Reorder the terms:
-25 + -3a + -3a + a2 = 25 + 3a + -25 + -3a

Combine like terms: -3a + -3a = -6a
-25 + -6a + a2 = 25 + 3a + -25 + -3a

Reorder the terms:
-25 + -6a + a2 = 25 + -25 + 3a + -3a

Combine like terms: 25 + -25 = 0
-25 + -6a + a2 = 0 + 3a + -3a
-25 + -6a + a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
-25 + -6a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6a + 25 + a2 = 0 + 25

Reorder the terms:
-25 + 25 + -6a + a2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6a + a2 = 0 + 25
-6a + a2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6a + a2 = 25

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 = 25 + 9

Reorder the terms:
9 + -6a + a2 = 25 + 9

Combine like terms: 25 + 9 = 34
9 + -6a + a2 = 34

Factor a perfect square on the left side:
(a + -3)(a + -3) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(a + -3) equal to 5.830951895 and -5.830951895.

Subproblem 1

a + -3 = 5.830951895 Simplifying a + -3 = 5.830951895 Reorder the terms: -3 + a = 5.830951895 Solving -3 + a = 5.830951895 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 = 5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + a = 5.830951895 + 3 a = 5.830951895 + 3 Combine like terms: 5.830951895 + 3 = 8.830951895 a = 8.830951895 Simplifying a = 8.830951895

Subproblem 2

a + -3 = -5.830951895 Simplifying a + -3 = -5.830951895 Reorder the terms: -3 + a = -5.830951895 Solving -3 + a = -5.830951895 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 = -5.830951895 + 3 Combine like terms: -3 + 3 = 0 0 + a = -5.830951895 + 3 a = -5.830951895 + 3 Combine like terms: -5.830951895 + 3 = -2.830951895 a = -2.830951895 Simplifying a = -2.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. a = {8.830951895, -2.830951895}

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