a^2+5a-3=0

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Solution for a^2+5a-3=0 equation:


Simplifying
a2 + 5a + -3 = 0

Reorder the terms:
-3 + 5a + a2 = 0

Solving
-3 + 5a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5a + 3 + a2 = 0 + 3

Reorder the terms:
-3 + 3 + 5a + a2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5a + a2 = 0 + 3
5a + a2 = 0 + 3

Combine like terms: 0 + 3 = 3
5a + a2 = 3

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = 3 + 6.25

Reorder the terms:
6.25 + 5a + a2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + 5a + a2 = 9.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(a + 2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

a + 2.5 = 3.041381265 Simplifying a + 2.5 = 3.041381265 Reorder the terms: 2.5 + a = 3.041381265 Solving 2.5 + a = 3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = 3.041381265 + -2.5 a = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 a = 0.541381265 Simplifying a = 0.541381265

Subproblem 2

a + 2.5 = -3.041381265 Simplifying a + 2.5 = -3.041381265 Reorder the terms: 2.5 + a = -3.041381265 Solving 2.5 + a = -3.041381265 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + a = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + a = -3.041381265 + -2.5 a = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 a = -5.541381265 Simplifying a = -5.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.541381265, -5.541381265}

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