r^2+64=r+144

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Solution for r^2+64=r+144 equation:


Simplifying
r2 + 64 = r + 144

Reorder the terms:
64 + r2 = r + 144

Reorder the terms:
64 + r2 = 144 + r

Solving
64 + r2 = 144 + r

Solving for variable 'r'.

Reorder the terms:
64 + -144 + -1r + r2 = 144 + r + -144 + -1r

Combine like terms: 64 + -144 = -80
-80 + -1r + r2 = 144 + r + -144 + -1r

Reorder the terms:
-80 + -1r + r2 = 144 + -144 + r + -1r

Combine like terms: 144 + -144 = 0
-80 + -1r + r2 = 0 + r + -1r
-80 + -1r + r2 = r + -1r

Combine like terms: r + -1r = 0
-80 + -1r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -1r + 80 + r2 = 0 + 80

Reorder the terms:
-80 + 80 + -1r + r2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -1r + r2 = 0 + 80
-1r + r2 = 0 + 80

Combine like terms: 0 + 80 = 80
-1r + r2 = 80

The r term is -1r.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1r + 0.25 + r2 = 80 + 0.25

Reorder the terms:
0.25 + -1r + r2 = 80 + 0.25

Combine like terms: 80 + 0.25 = 80.25
0.25 + -1r + r2 = 80.25

Factor a perfect square on the left side:
(r + -0.5)(r + -0.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(r + -0.5) equal to 8.958236434 and -8.958236434.

Subproblem 1

r + -0.5 = 8.958236434 Simplifying r + -0.5 = 8.958236434 Reorder the terms: -0.5 + r = 8.958236434 Solving -0.5 + r = 8.958236434 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = 8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = 8.958236434 + 0.5 r = 8.958236434 + 0.5 Combine like terms: 8.958236434 + 0.5 = 9.458236434 r = 9.458236434 Simplifying r = 9.458236434

Subproblem 2

r + -0.5 = -8.958236434 Simplifying r + -0.5 = -8.958236434 Reorder the terms: -0.5 + r = -8.958236434 Solving -0.5 + r = -8.958236434 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + r = -8.958236434 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + r = -8.958236434 + 0.5 r = -8.958236434 + 0.5 Combine like terms: -8.958236434 + 0.5 = -8.458236434 r = -8.458236434 Simplifying r = -8.458236434

Solution

The solution to the problem is based on the solutions from the subproblems. r = {9.458236434, -8.458236434}

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