0=5a^2-16a-37

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Solution for 0=5a^2-16a-37 equation:


Simplifying
0 = 5a2 + -16a + -37

Reorder the terms:
0 = -37 + -16a + 5a2

Solving
0 = -37 + -16a + 5a2

Solving for variable 'a'.

Combine like terms: 0 + 37 = 37
37 + 16a + -5a2 = -37 + -16a + 5a2 + 37 + 16a + -5a2

Reorder the terms:
37 + 16a + -5a2 = -37 + 37 + -16a + 16a + 5a2 + -5a2

Combine like terms: -37 + 37 = 0
37 + 16a + -5a2 = 0 + -16a + 16a + 5a2 + -5a2
37 + 16a + -5a2 = -16a + 16a + 5a2 + -5a2

Combine like terms: -16a + 16a = 0
37 + 16a + -5a2 = 0 + 5a2 + -5a2
37 + 16a + -5a2 = 5a2 + -5a2

Combine like terms: 5a2 + -5a2 = 0
37 + 16a + -5a2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-7.4 + -3.2a + a2 = 0

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + -3.2a + 7.4 + a2 = 0 + 7.4

Reorder the terms:
-7.4 + 7.4 + -3.2a + a2 = 0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + -3.2a + a2 = 0 + 7.4
-3.2a + a2 = 0 + 7.4

Combine like terms: 0 + 7.4 = 7.4
-3.2a + a2 = 7.4

The a term is -3.2a.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2a + 2.56 + a2 = 7.4 + 2.56

Reorder the terms:
2.56 + -3.2a + a2 = 7.4 + 2.56

Combine like terms: 7.4 + 2.56 = 9.96
2.56 + -3.2a + a2 = 9.96

Factor a perfect square on the left side:
(a + -1.6)(a + -1.6) = 9.96

Calculate the square root of the right side: 3.155946768

Break this problem into two subproblems by setting 
(a + -1.6) equal to 3.155946768 and -3.155946768.

Subproblem 1

a + -1.6 = 3.155946768 Simplifying a + -1.6 = 3.155946768 Reorder the terms: -1.6 + a = 3.155946768 Solving -1.6 + a = 3.155946768 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = 3.155946768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = 3.155946768 + 1.6 a = 3.155946768 + 1.6 Combine like terms: 3.155946768 + 1.6 = 4.755946768 a = 4.755946768 Simplifying a = 4.755946768

Subproblem 2

a + -1.6 = -3.155946768 Simplifying a + -1.6 = -3.155946768 Reorder the terms: -1.6 + a = -3.155946768 Solving -1.6 + a = -3.155946768 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = -3.155946768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = -3.155946768 + 1.6 a = -3.155946768 + 1.6 Combine like terms: -3.155946768 + 1.6 = -1.555946768 a = -1.555946768 Simplifying a = -1.555946768

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.755946768, -1.555946768}

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