15a^2-3a-8=0

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Solution for 15a^2-3a-8=0 equation:


Simplifying
15a2 + -3a + -8 = 0

Reorder the terms:
-8 + -3a + 15a2 = 0

Solving
-8 + -3a + 15a2 = 0

Solving for variable 'a'.

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

Divide each side by '15'.
-0.5333333333 + -0.2a + a2 = 0

Move the constant term to the right:

Add '0.5333333333' to each side of the equation.
-0.5333333333 + -0.2a + 0.5333333333 + a2 = 0 + 0.5333333333

Reorder the terms:
-0.5333333333 + 0.5333333333 + -0.2a + a2 = 0 + 0.5333333333

Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000
0.0000000000 + -0.2a + a2 = 0 + 0.5333333333
-0.2a + a2 = 0 + 0.5333333333

Combine like terms: 0 + 0.5333333333 = 0.5333333333
-0.2a + a2 = 0.5333333333

The a term is -0.2a.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2a + 0.01 + a2 = 0.5333333333 + 0.01

Reorder the terms:
0.01 + -0.2a + a2 = 0.5333333333 + 0.01

Combine like terms: 0.5333333333 + 0.01 = 0.5433333333
0.01 + -0.2a + a2 = 0.5433333333

Factor a perfect square on the left side:
(a + -0.1)(a + -0.1) = 0.5433333333

Calculate the square root of the right side: 0.73711148

Break this problem into two subproblems by setting 
(a + -0.1) equal to 0.73711148 and -0.73711148.

Subproblem 1

a + -0.1 = 0.73711148 Simplifying a + -0.1 = 0.73711148 Reorder the terms: -0.1 + a = 0.73711148 Solving -0.1 + a = 0.73711148 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = 0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = 0.73711148 + 0.1 a = 0.73711148 + 0.1 Combine like terms: 0.73711148 + 0.1 = 0.83711148 a = 0.83711148 Simplifying a = 0.83711148

Subproblem 2

a + -0.1 = -0.73711148 Simplifying a + -0.1 = -0.73711148 Reorder the terms: -0.1 + a = -0.73711148 Solving -0.1 + a = -0.73711148 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + a = -0.73711148 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + a = -0.73711148 + 0.1 a = -0.73711148 + 0.1 Combine like terms: -0.73711148 + 0.1 = -0.63711148 a = -0.63711148 Simplifying a = -0.63711148

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.83711148, -0.63711148}

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