Question
Solve the equation
r1=−25+17,r2=2−5+17
Alternative Form
r1≈−4.561553,r2≈−0.438447
Evaluate
r7−5=(3×r2r)−2r−15
Find the domain
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Evaluate
{r=0r2=0
The only way a power can not be 0 is when the base not equals 0
{r=0r=0
Find the intersection
r=0
r7−5=(3×r2r)−2r−15,r=0
Simplify
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Evaluate
(3×r2r)−2r−15
Divide the terms
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Evaluate
r2r
Use the product rule aman=an−m to simplify the expression
r2−11
Reduce the fraction
r1
(3×r1)−2r−15
Multiply the terms
r3−2r−15
r7−5=r3−2r−15
Multiply both sides of the equation by LCD
(r7−5)r=(r3−2r−15)r
Simplify the equation
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Evaluate
(r7−5)r
Apply the distributive property
r7×r−5r
Simplify
7−5r
7−5r=(r3−2r−15)r
Simplify the equation
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Evaluate
(r3−2r−15)r
Apply the distributive property
r3×r−2r×r−15r
Simplify
3−2r×r−15r
Multiply the terms
3−2r2−15r
7−5r=3−2r2−15r
Move the expression to the left side
7−5r−(3−2r2−15r)=0
Subtract the terms
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Evaluate
7−5r−(3−2r2−15r)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
7−5r−3+2r2+15r
Subtract the numbers
4−5r+2r2+15r
Add the terms
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Evaluate
−5r+15r
Collect like terms by calculating the sum or difference of their coefficients
(−5+15)r
Add the numbers
10r
4+10r+2r2
4+10r+2r2=0
Rewrite in standard form
2r2+10r+4=0
Substitute a=2,b=10 and c=4 into the quadratic formula r=2a−b±b2−4ac
r=2×2−10±102−4×2×4
Simplify the expression
r=4−10±102−4×2×4
Simplify the expression
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Evaluate
102−4×2×4
Multiply the terms
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Multiply the terms
4×2×4
Multiply the terms
8×4
Multiply the numbers
32
102−32
Evaluate the power
100−32
Subtract the numbers
68
r=4−10±68
Simplify the radical expression
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Evaluate
68
Write the expression as a product where the root of one of the factors can be evaluated
4×17
Write the number in exponential form with the base of 2
22×17
The root of a product is equal to the product of the roots of each factor
22×17
Reduce the index of the radical and exponent with 2
217
r=4−10±217
Separate the equation into 2 possible cases
r=4−10+217r=4−10−217
Simplify the expression
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Evaluate
r=4−10+217
Divide the terms
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Evaluate
4−10+217
Rewrite the expression
42(−5+17)
Cancel out the common factor 2
2−5+17
r=2−5+17
r=2−5+17r=4−10−217
Simplify the expression
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Evaluate
r=4−10−217
Divide the terms
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Evaluate
4−10−217
Rewrite the expression
42(−5−17)
Cancel out the common factor 2
2−5−17
Use b−a=−ba=−ba to rewrite the fraction
−25+17
r=−25+17
r=2−5+17r=−25+17
Check if the solution is in the defined range
r=2−5+17r=−25+17,r=0
Find the intersection of the solution and the defined range
r=2−5+17r=−25+17
Solution
r1=−25+17,r2=2−5+17
Alternative Form
r1≈−4.561553,r2≈−0.438447
Show Solution

Rewrite the equation
21x2+21y2=x4+y4+4+2x2y2
Evaluate
r7−5=(3×r2r)−2r−15
Evaluate
More Steps

Evaluate
(3×r2r)−2r−15
Divide the terms
More Steps

Evaluate
r2r
Use the product rule aman=an−m to simplify the expression
r2−11
Reduce the fraction
r1
(3×r1)−2r−15
Multiply the terms
r3−2r−15
r7−5=r3−2r−15
Multiply both sides of the equation by LCD
(r7−5)r=(r3−2r−15)r
Simplify the equation
More Steps

Evaluate
(r7−5)r
Apply the distributive property
r7×r−5r
Simplify
7−5r
7−5r=(r3−2r−15)r
Simplify the equation
More Steps

Evaluate
(r3−2r−15)r
Apply the distributive property
r3×r−2r×r−15r
Simplify
3−2r×r−15r
Multiply the terms
3−2r2−15r
7−5r=3−2r2−15r
Rewrite the expression
10r+2r2=−7+3
Simplify the expression
10r+2r2=−4
Use substitution
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Evaluate
10r+2r2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
10r+2(x2+y2)
Simplify the expression
10r+2x2+2y2
10r+2x2+2y2=−4
Simplify the expression
10r=−2x2−2y2−4
Square both sides of the equation
(10r)2=(−2x2−2y2−4)2
Evaluate
100r2=(−2x2−2y2−4)2
To covert the equation to rectangular coordinates using conversion formulas,substitute x2+y2 for r2
100(x2+y2)=(−2x2−2y2−4)2
Evaluate the power
100(x2+y2)=(2x2+2y2+4)2
Divide both sides of the equation by 4
25(x2+y2)=(x2+y2+2)2
Calculate
25x2+25y2=x4+y4+4+2x2y2+4x2+4y2
Move the expression to the left side
25x2+25y2−(4x2+4y2)=x4+y4+4+2x2y2
Calculate
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Evaluate
25x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(25−4)x2
Subtract the numbers
21x2
21x2+25y2=x4+y4+4+2x2y2+4y2
Solution
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Evaluate
25y2−4y2
Collect like terms by calculating the sum or difference of their coefficients
(25−4)y2
Subtract the numbers
21y2
21x2+21y2=x4+y4+4+2x2y2
Show Solution
