24a^2+a-15=0

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Solution for 24a^2+a-15=0 equation:


Simplifying
24a2 + a + -15 = 0

Reorder the terms:
-15 + a + 24a2 = 0

Solving
-15 + a + 24a2 = 0

Solving for variable 'a'.

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

Divide each side by '24'.
-0.625 + 0.04166666667a + a2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 0.04166666667a + 0.625 + a2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 0.04166666667a + a2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 0.04166666667a + a2 = 0 + 0.625
0.04166666667a + a2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
0.04166666667a + a2 = 0.625

The a term is a.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.04166666667a + 0.25 + a2 = 0.625 + 0.25

Reorder the terms:
0.25 + 0.04166666667a + a2 = 0.625 + 0.25

Combine like terms: 0.625 + 0.25 = 0.875
0.25 + 0.04166666667a + a2 = 0.875

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 0.875

Calculate the square root of the right side: 0.935414347

Break this problem into two subproblems by setting 
(a + 0.5) equal to 0.935414347 and -0.935414347.

Subproblem 1

a + 0.5 = 0.935414347 Simplifying a + 0.5 = 0.935414347 Reorder the terms: 0.5 + a = 0.935414347 Solving 0.5 + a = 0.935414347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.935414347 + -0.5 a = 0.935414347 + -0.5 Combine like terms: 0.935414347 + -0.5 = 0.435414347 a = 0.435414347 Simplifying a = 0.435414347

Subproblem 2

a + 0.5 = -0.935414347 Simplifying a + 0.5 = -0.935414347 Reorder the terms: 0.5 + a = -0.935414347 Solving 0.5 + a = -0.935414347 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.935414347 + -0.5 a = -0.935414347 + -0.5 Combine like terms: -0.935414347 + -0.5 = -1.435414347 a = -1.435414347 Simplifying a = -1.435414347

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.435414347, -1.435414347}

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