4a^2+7a-3=0

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Solution for 4a^2+7a-3=0 equation: 


Simplifying
4a2 + 7a + -3 = 0

Reorder the terms:
-3 + 7a + 4a2 = 0

Solving
-3 + 7a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
-0.75 + 1.75a + a2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 1.75a + 0.75 + a2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 1.75a + a2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 1.75a + a2 = 0 + 0.75
1.75a + a2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
1.75a + a2 = 0.75

The a term is 1.75a.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75a + 0.765625 + a2 = 0.75 + 0.765625

Reorder the terms:
0.765625 + 1.75a + a2 = 0.75 + 0.765625

Combine like terms: 0.75 + 0.765625 = 1.515625
0.765625 + 1.75a + a2 = 1.515625

Factor a perfect square on the left side:
(a + 0.875)(a + 0.875) = 1.515625

Calculate the square root of the right side: 1.231107225

Break this problem into two subproblems by setting 
(a + 0.875) equal to 1.231107225 and -1.231107225.


Subproblem 1
a + 0.875 = 1.231107225

Simplifying
a + 0.875 = 1.231107225

Reorder the terms:
0.875 + a = 1.231107225

Solving
0.875 + a = 1.231107225

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + a = 1.231107225 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + a = 1.231107225 + -0.875
a = 1.231107225 + -0.875

Combine like terms: 1.231107225 + -0.875 = 0.356107225
a = 0.356107225

Simplifying
a = 0.356107225


Subproblem 2
a + 0.875 = -1.231107225

Simplifying
a + 0.875 = -1.231107225

Reorder the terms:
0.875 + a = -1.231107225

Solving
0.875 + a = -1.231107225

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + a = -1.231107225 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + a = -1.231107225 + -0.875
a = -1.231107225 + -0.875

Combine like terms: -1.231107225 + -0.875 = -2.106107225
a = -2.106107225

Simplifying
a = -2.106107225


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.356107225, -2.106107225}

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