8a^2+3a-15=0

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


Simplifying
8a2 + 3a + -15 = 0

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

Solving
-15 + 3a + 8a2 = 0

Solving for variable 'a'.

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

Divide each side by '8'.
-1.875 + 0.375a + a2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.375a + 1.875 + a2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.375a + a2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.375a + a2 = 0 + 1.875
0.375a + a2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.375a + a2 = 1.875

The a term is 0.375a.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375a + 0.03515625 + a2 = 1.875 + 0.03515625

Reorder the terms:
0.03515625 + 0.375a + a2 = 1.875 + 0.03515625

Combine like terms: 1.875 + 0.03515625 = 1.91015625
0.03515625 + 0.375a + a2 = 1.91015625

Factor a perfect square on the left side:
(a + 0.1875)(a + 0.1875) = 1.91015625

Calculate the square root of the right side: 1.382084024

Break this problem into two subproblems by setting 
(a + 0.1875) equal to 1.382084024 and -1.382084024.

Subproblem 1

a + 0.1875 = 1.382084024 Simplifying a + 0.1875 = 1.382084024 Reorder the terms: 0.1875 + a = 1.382084024 Solving 0.1875 + a = 1.382084024 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = 1.382084024 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = 1.382084024 + -0.1875 a = 1.382084024 + -0.1875 Combine like terms: 1.382084024 + -0.1875 = 1.194584024 a = 1.194584024 Simplifying a = 1.194584024

Subproblem 2

a + 0.1875 = -1.382084024 Simplifying a + 0.1875 = -1.382084024 Reorder the terms: 0.1875 + a = -1.382084024 Solving 0.1875 + a = -1.382084024 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + a = -1.382084024 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + a = -1.382084024 + -0.1875 a = -1.382084024 + -0.1875 Combine like terms: -1.382084024 + -0.1875 = -1.569584024 a = -1.569584024 Simplifying a = -1.569584024

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.194584024, -1.569584024}

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