Solve Using the Square Root Property 2420=2000(1+r)^2

Math
2420=2000(1+r)2
Rewrite the equation as 2000(1+r)2=2420.
2000(1+r)2=2420
Divide each term by 2000 and simplify.
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Divide each term in 2000(1+r)2=2420 by 2000.
2000(1+r)22000=24202000
Cancel the common factor of 2000.
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Cancel the common factor.
2000(1+r)22000=24202000
Divide (1+r)2 by 1.
(1+r)2=24202000
(1+r)2=24202000
Cancel the common factor of 2420 and 2000.
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Factor 20 out of 2420.
(1+r)2=20(121)2000
Cancel the common factors.
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Factor 20 out of 2000.
(1+r)2=20⋅12120⋅100
Cancel the common factor.
(1+r)2=20⋅12120⋅100
Rewrite the expression.
(1+r)2=121100
(1+r)2=121100
(1+r)2=121100
(1+r)2=121100
Take the square root of each side of the equation to set up the solution for r
(1+r)2⋅12=±121100
Remove the perfect root factor 1+r under the radical to solve for r.
1+r=±121100
Simplify the right side of the equation.
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Rewrite 121100 as 121100.
1+r=±121100
Simplify the numerator.
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Rewrite 121 as 112.
1+r=±112100
Pull terms out from under the radical, assuming positive real numbers.
1+r=±11100
1+r=±11100
Simplify the denominator.
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Rewrite 100 as 102.
1+r=±11102
Pull terms out from under the radical, assuming positive real numbers.
1+r=±1110
1+r=±1110
1+r=±1110
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the ± to find the first solution.
1+r=1110
Move all terms not containing r to the right side of the equation.
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Subtract 1 from both sides of the equation.
r=1110-1
To write -1 as a fraction with a common denominator, multiply by 1010.
r=1110-1⋅1010
Combine -1 and 1010.
r=1110+-1⋅1010
Combine the numerators over the common denominator.
r=11-1⋅1010
Simplify the numerator.
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Multiply -1 by 10.
r=11-1010
Subtract 10 from 11.
r=110
r=110
r=110
Next, use the negative value of the ± to find the second solution.
1+r=-1110
Move all terms not containing r to the right side of the equation.
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Subtract 1 from both sides of the equation.
r=-1110-1
To write -1 as a fraction with a common denominator, multiply by 1010.
r=-1110-1⋅1010
Combine -1 and 1010.
r=-1110+-1⋅1010
Combine the numerators over the common denominator.
r=-11-1⋅1010
Simplify the numerator.
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Multiply -1 by 10.
r=-11-1010
Subtract 10 from -11.
r=-2110
r=-2110
Move the negative in front of the fraction.
r=-2110
r=-2110
The complete solution is the result of both the positive and negative portions of the solution.
r=110,-2110
r=110,-2110
Solve Using the Square Root Property 2420=2000(1+r)^2

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