Question
Solve the equation
r=1930
Alternative Form
r≈1.578947
Evaluate
512+2512r=3+101r
Multiply both sides of the equation by LCM
(512+2512r)×50=(3+101r)×50
Calculate
More Steps

Evaluate
(512+2512r)×50
Apply the distributive property
512×50+2512r×50
Multiply the numbers
More Steps

Evaluate
512×50
Reduce the numbers
12×10
Multiply the numbers
120
120+2512r×50
Multiply the numbers
More Steps

Evaluate
2512×50
Reduce the numbers
12×2
Multiply the numbers
24
120+24r
120+24r=(3+101r)×50
Calculate
More Steps

Evaluate
(3+101r)×50
Apply the distributive property
3×50+101r×50
Multiply the numbers
150+101r×50
Multiply the numbers
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Evaluate
101×50
Reduce the numbers
1×5
Simplify
5
150+5r
120+24r=150+5r
Move the expression to the left side
120+24r−5r=150
Move the expression to the right side
24r−5r=150−120
Add and subtract
More Steps

Evaluate
24r−5r
Collect like terms by calculating the sum or difference of their coefficients
(24−5)r
Subtract the numbers
19r
19r=150−120
Add and subtract
19r=30
Divide both sides
1919r=1930
Solution
r=1930
Alternative Form
r≈1.578947
Show Solution

Rewrite the equation
361x2+361y2=900
Evaluate
512+2512r=3+101r
Multiply both sides of the equation by LCD
(512+2512r)×50=(3+101r)×50
Simplify the equation
More Steps

Evaluate
(512+2512r)×50
Apply the distributive property
512×50+2512r×50
Simplify
12×10+12r×2
Multiply the numbers
120+12r×2
Multiply the numbers
120+24r
120+24r=(3+101r)×50
Simplify the equation
More Steps

Evaluate
(3+101r)×50
Apply the distributive property
3×50+101r×50
Simplify
3×50+r×5
Multiply the numbers
150+r×5
Use the commutative property to reorder the terms
150+5r
120+24r=150+5r
Rewrite the expression
19r=−120+150
Simplify the expression
19r=30
Square both sides of the equation
(19r)2=302
Evaluate
361r2=302
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
361(x2+y2)=302
Evaluate the power
361(x2+y2)=900
Solution
361x2+361y2=900
Show Solution
