4r^2-36r+49=

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Solution for 4r^2-36r+49= equation:


Simplifying
4r2 + -36r + 49 = 0

Reorder the terms:
49 + -36r + 4r2 = 0

Solving
49 + -36r + 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'.
12.25 + -9r + r2 = 0

Move the constant term to the right:

Add '-12.25' to each side of the equation.
12.25 + -9r + -12.25 + r2 = 0 + -12.25

Reorder the terms:
12.25 + -12.25 + -9r + r2 = 0 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
0.00 + -9r + r2 = 0 + -12.25
-9r + r2 = 0 + -12.25

Combine like terms: 0 + -12.25 = -12.25
-9r + r2 = -12.25

The r term is -9r.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9r + 20.25 + r2 = -12.25 + 20.25

Reorder the terms:
20.25 + -9r + r2 = -12.25 + 20.25

Combine like terms: -12.25 + 20.25 = 8
20.25 + -9r + r2 = 8

Factor a perfect square on the left side:
(r + -4.5)(r + -4.5) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(r + -4.5) equal to 2.828427125 and -2.828427125.

Subproblem 1

r + -4.5 = 2.828427125 Simplifying r + -4.5 = 2.828427125 Reorder the terms: -4.5 + r = 2.828427125 Solving -4.5 + r = 2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = 2.828427125 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = 2.828427125 + 4.5 r = 2.828427125 + 4.5 Combine like terms: 2.828427125 + 4.5 = 7.328427125 r = 7.328427125 Simplifying r = 7.328427125

Subproblem 2

r + -4.5 = -2.828427125 Simplifying r + -4.5 = -2.828427125 Reorder the terms: -4.5 + r = -2.828427125 Solving -4.5 + r = -2.828427125 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + r = -2.828427125 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + r = -2.828427125 + 4.5 r = -2.828427125 + 4.5 Combine like terms: -2.828427125 + 4.5 = 1.671572875 r = 1.671572875 Simplifying r = 1.671572875

Solution

The solution to the problem is based on the solutions from the subproblems. r = {7.328427125, 1.671572875}

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