.5a^2+a-4=0

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Solution for .5a^2+a-4=0 equation:


Simplifying
0.5a2 + a + -4 = 0

Reorder the terms:
-4 + a + 0.5a2 = 0

Solving
-4 + a + 0.5a2 = 0

Solving for variable 'a'.

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

Divide each side by '0.5'.
-8 + 2a + a2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 2a + 8 + a2 = 0 + 8

Reorder the terms:
-8 + 8 + 2a + a2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 2a + a2 = 0 + 8
2a + a2 = 0 + 8

Combine like terms: 0 + 8 = 8
2a + a2 = 8

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.
2a + 0.25 + a2 = 8 + 0.25

Reorder the terms:
0.25 + 2a + a2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + 2a + a2 = 8.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(a + 0.5) equal to 2.872281323 and -2.872281323.

Subproblem 1

a + 0.5 = 2.872281323 Simplifying a + 0.5 = 2.872281323 Reorder the terms: 0.5 + a = 2.872281323 Solving 0.5 + a = 2.872281323 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 = 2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 2.872281323 + -0.5 a = 2.872281323 + -0.5 Combine like terms: 2.872281323 + -0.5 = 2.372281323 a = 2.372281323 Simplifying a = 2.372281323

Subproblem 2

a + 0.5 = -2.872281323 Simplifying a + 0.5 = -2.872281323 Reorder the terms: 0.5 + a = -2.872281323 Solving 0.5 + a = -2.872281323 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 = -2.872281323 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -2.872281323 + -0.5 a = -2.872281323 + -0.5 Combine like terms: -2.872281323 + -0.5 = -3.372281323 a = -3.372281323 Simplifying a = -3.372281323

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.372281323, -3.372281323}

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