5r^2+7r-4=0

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Solution for 5r^2+7r-4=0 equation:


Simplifying
5r2 + 7r + -4 = 0

Reorder the terms:
-4 + 7r + 5r2 = 0

Solving
-4 + 7r + 5r2 = 0

Solving for variable 'r'.

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

Divide each side by '5'.
-0.8 + 1.4r + r2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 1.4r + 0.8 + r2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 1.4r + r2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 1.4r + r2 = 0 + 0.8
1.4r + r2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
1.4r + r2 = 0.8

The r term is 1.4r.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4r + 0.49 + r2 = 0.8 + 0.49

Reorder the terms:
0.49 + 1.4r + r2 = 0.8 + 0.49

Combine like terms: 0.8 + 0.49 = 1.29
0.49 + 1.4r + r2 = 1.29

Factor a perfect square on the left side:
(r + 0.7)(r + 0.7) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(r + 0.7) equal to 1.135781669 and -1.135781669.

Subproblem 1

r + 0.7 = 1.135781669 Simplifying r + 0.7 = 1.135781669 Reorder the terms: 0.7 + r = 1.135781669 Solving 0.7 + r = 1.135781669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = 1.135781669 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = 1.135781669 + -0.7 r = 1.135781669 + -0.7 Combine like terms: 1.135781669 + -0.7 = 0.435781669 r = 0.435781669 Simplifying r = 0.435781669

Subproblem 2

r + 0.7 = -1.135781669 Simplifying r + 0.7 = -1.135781669 Reorder the terms: 0.7 + r = -1.135781669 Solving 0.7 + r = -1.135781669 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + r = -1.135781669 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + r = -1.135781669 + -0.7 r = -1.135781669 + -0.7 Combine like terms: -1.135781669 + -0.7 = -1.835781669 r = -1.835781669 Simplifying r = -1.835781669

Solution

The solution to the problem is based on the solutions from the subproblems. r = {0.435781669, -1.835781669}

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