8a*a+37a-15=a

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Solution for 8a*a+37a-15=a equation:


Simplifying
8a * a + 37a + -15 = a

Multiply a * a
8a2 + 37a + -15 = a

Reorder the terms:
-15 + 37a + 8a2 = a

Solving
-15 + 37a + 8a2 = a

Solving for variable 'a'.

Reorder the terms:
-15 + 37a + -1a + 8a2 = a + -1a

Combine like terms: 37a + -1a = 36a
-15 + 36a + 8a2 = a + -1a

Combine like terms: a + -1a = 0
-15 + 36a + 8a2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-1.875 + 4.5a + a2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 4.5a + 1.875 + a2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 4.5a + a2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 4.5a + a2 = 0 + 1.875
4.5a + a2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
4.5a + a2 = 1.875

The a term is 4.5a.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5a + 5.0625 + a2 = 1.875 + 5.0625

Reorder the terms:
5.0625 + 4.5a + a2 = 1.875 + 5.0625

Combine like terms: 1.875 + 5.0625 = 6.9375
5.0625 + 4.5a + a2 = 6.9375

Factor a perfect square on the left side:
(a + 2.25)(a + 2.25) = 6.9375

Calculate the square root of the right side: 2.633913438

Break this problem into two subproblems by setting 
(a + 2.25) equal to 2.633913438 and -2.633913438.

Subproblem 1

a + 2.25 = 2.633913438 Simplifying a + 2.25 = 2.633913438 Reorder the terms: 2.25 + a = 2.633913438 Solving 2.25 + a = 2.633913438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = 2.633913438 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = 2.633913438 + -2.25 a = 2.633913438 + -2.25 Combine like terms: 2.633913438 + -2.25 = 0.383913438 a = 0.383913438 Simplifying a = 0.383913438

Subproblem 2

a + 2.25 = -2.633913438 Simplifying a + 2.25 = -2.633913438 Reorder the terms: 2.25 + a = -2.633913438 Solving 2.25 + a = -2.633913438 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + a = -2.633913438 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + a = -2.633913438 + -2.25 a = -2.633913438 + -2.25 Combine like terms: -2.633913438 + -2.25 = -4.883913438 a = -4.883913438 Simplifying a = -4.883913438

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.383913438, -4.883913438}

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