# Solve for r (1.68)^32=(1+r/4)^32 (1.68)32=(1+r4)32
Rewrite the equation as (1+r4)32=(1.68)32.
(1+r4)32=(1.68)32
Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.
|1+r4|=|1.68|
Solve for r.
The absolute value is the distance between a number and zero. The distance between 0 and 1.68 is 1.68.
|1+r4|=1.68
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
1+r4=±1.68
Set up the positive portion of the ± solution.
1+r4=1.68
Solve the first equation for r.
Move all terms not containing r to the right side of the equation.
Subtract 1 from both sides of the equation.
r4=1.68-1
Subtract 1 from 1.68.
r4=0.68
r4=0.68
Multiply both sides of the equation by 4.
4⋅r4=4⋅0.68
Simplify both sides of the equation.
Cancel the common factor of 4.
Cancel the common factor.
4⋅r4=4⋅0.68
Rewrite the expression.
r=4⋅0.68
r=4⋅0.68
Multiply 4 by 0.68.
r=2.72
r=2.72
r=2.72
Set up the negative portion of the ± solution.
1+r4=-1.68
Solve the second equation for r.
Move all terms not containing r to the right side of the equation.
Subtract 1 from both sides of the equation.
r4=-1.68-1
Subtract 1 from -1.68.
r4=-2.68
r4=-2.68
Multiply both sides of the equation by 4.
4⋅r4=4⋅-2.68
Simplify both sides of the equation.
Cancel the common factor of 4.
Cancel the common factor.
4⋅r4=4⋅-2.68
Rewrite the expression.
r=4⋅-2.68
r=4⋅-2.68
Multiply 4 by -2.68.
r=-10.72
r=-10.72
r=-10.72
The solution to the equation includes both the positive and negative portions of the solution.
r=2.72,-10.72
r=2.72,-10.72
Solve for r (1.68)^32=(1+r/4)^32

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