4r^2-7r-3=0

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


Simplifying
4r2 + -7r + -3 = 0

Reorder the terms:
-3 + -7r + 4r2 = 0

Solving
-3 + -7r + 4r2 = 0

Solving for variable 'r'.

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

Divide each side by '4'.
-0.75 + -1.75r + r2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -1.75r + 0.75 + r2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -1.75r + r2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -1.75r + r2 = 0 + 0.75
-1.75r + r2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-1.75r + r2 = 0.75

The r term is -1.75r.  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.
-1.75r + 0.765625 + r2 = 0.75 + 0.765625

Reorder the terms:
0.765625 + -1.75r + r2 = 0.75 + 0.765625

Combine like terms: 0.75 + 0.765625 = 1.515625
0.765625 + -1.75r + r2 = 1.515625

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

Calculate the square root of the right side: 1.231107225

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


Subproblem 1
r + -0.875 = 1.231107225

Simplifying
r + -0.875 = 1.231107225

Reorder the terms:
-0.875 + r = 1.231107225

Solving
-0.875 + r = 1.231107225

Solving for variable 'r'.

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

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

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

Combine like terms: 1.231107225 + 0.875 = 2.106107225
r = 2.106107225

Simplifying
r = 2.106107225


Subproblem 2
r + -0.875 = -1.231107225

Simplifying
r + -0.875 = -1.231107225

Reorder the terms:
-0.875 + r = -1.231107225

Solving
-0.875 + r = -1.231107225

Solving for variable 'r'.

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

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

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

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

Simplifying
r = -0.356107225


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

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