4r^2-9r+4=0

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Solution for 4r^2-9r+4=0 equation:


Simplifying
4r2 + -9r + 4 = 0

Reorder the terms:
4 + -9r + 4r2 = 0

Solving
4 + -9r + 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'.
1 + -2.25r + r2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.25r + -1 + r2 = 0 + -1

Reorder the terms:
1 + -1 + -2.25r + r2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.25r + r2 = 0 + -1
-2.25r + r2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.25r + r2 = -1

The r term is -2.25r.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25r + 1.265625 + r2 = -1 + 1.265625

Reorder the terms:
1.265625 + -2.25r + r2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + -2.25r + r2 = 0.265625

Factor a perfect square on the left side:
(r + -1.125)(r + -1.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(r + -1.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

r + -1.125 = 0.515388203 Simplifying r + -1.125 = 0.515388203 Reorder the terms: -1.125 + r = 0.515388203 Solving -1.125 + r = 0.515388203 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + r = 0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + r = 0.515388203 + 1.125 r = 0.515388203 + 1.125 Combine like terms: 0.515388203 + 1.125 = 1.640388203 r = 1.640388203 Simplifying r = 1.640388203

Subproblem 2

r + -1.125 = -0.515388203 Simplifying r + -1.125 = -0.515388203 Reorder the terms: -1.125 + r = -0.515388203 Solving -1.125 + r = -0.515388203 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + r = -0.515388203 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + r = -0.515388203 + 1.125 r = -0.515388203 + 1.125 Combine like terms: -0.515388203 + 1.125 = 0.609611797 r = 0.609611797 Simplifying r = 0.609611797

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.640388203, 0.609611797}

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