(52)2=(3(2)4)2+x2

Rewrite the equation as (3(2)4)2+x2=(52)2.

(3(2)4)2+x2=(52)2

Use the power rule (ab)n=anbn to distribute the exponent.

Apply the product rule to 324.

(32)242+x2=(52)2

Apply the product rule to 32.

322242+x2=(52)2

322242+x2=(52)2

Simplify the numerator.

Raise 3 to the power of 2.

92242+x2=(52)2

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

9(212)242+x2=(52)2

Apply the power rule and multiply exponents, (am)n=amn.

9⋅212⋅242+x2=(52)2

Combine 12 and 2.

9⋅22242+x2=(52)2

Cancel the common factor of 2.

Cancel the common factor.

9⋅22242+x2=(52)2

Divide 1 by 1.

9⋅2142+x2=(52)2

9⋅2142+x2=(52)2

Evaluate the exponent.

9⋅242+x2=(52)2

9⋅242+x2=(52)2

9⋅242+x2=(52)2

Raise 4 to the power of 2.

9⋅216+x2=(52)2

Multiply 9 by 2.

1816+x2=(52)2

Cancel the common factor of 18 and 16.

Factor 2 out of 18.

2(9)16+x2=(52)2

Cancel the common factors.

Factor 2 out of 16.

2⋅92⋅8+x2=(52)2

Cancel the common factor.

2⋅92⋅8+x2=(52)2

Rewrite the expression.

98+x2=(52)2

98+x2=(52)2

98+x2=(52)2

98+x2=(52)2

Apply the product rule to 52.

98+x2=5222

Rewrite 52 as 5.

Use axn=axn to rewrite 5 as 512.

98+x2=(512)222

Apply the power rule and multiply exponents, (am)n=amn.

98+x2=512⋅222

Combine 12 and 2.

98+x2=52222

Cancel the common factor of 2.

Cancel the common factor.

98+x2=52222

Divide 1 by 1.

98+x2=5122

98+x2=5122

Evaluate the exponent.

98+x2=522

98+x2=522

Raise 2 to the power of 2.

98+x2=54

98+x2=54

Subtract 98 from both sides of the equation.

x2=54-98

To write 54 as a fraction with a common denominator, multiply by 22.

x2=54⋅22-98

Write each expression with a common denominator of 8, by multiplying each by an appropriate factor of 1.

Multiply 54 and 22.

x2=5⋅24⋅2-98

Multiply 4 by 2.

x2=5⋅28-98

x2=5⋅28-98

Combine the numerators over the common denominator.

x2=5⋅2-98

Simplify the numerator.

Multiply 5 by 2.

x2=10-98

Subtract 9 from 10.

x2=18

x2=18

x2=18

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x=±18

Simplify the right side of the equation.

Rewrite 18 as 18.

x=±18

Any root of 1 is 1.

x=±18

Simplify the denominator.

Rewrite 8 as 22⋅2.

Factor 4 out of 8.

x=±14(2)

Rewrite 4 as 22.

x=±122⋅2

x=±122⋅2

Pull terms out from under the radical.

x=±122

x=±122

Multiply 122 by 22.

x=±122⋅22

Combine and simplify the denominator.

Multiply 122 and 22.

x=±2222

Move 2.

x=±22(22)

Raise 2 to the power of 1.

x=±22(22)

Raise 2 to the power of 1.

x=±22(22)

Use the power rule aman=am+n to combine exponents.

x=±2221+1

Add 1 and 1.

x=±2222

Rewrite 22 as 2.

Use axn=axn to rewrite 2 as 212.

x=±22(212)2

Apply the power rule and multiply exponents, (am)n=amn.

x=±22⋅212⋅2

Combine 12 and 2.

x=±22⋅222

Cancel the common factor of 2.

Cancel the common factor.

x=±22⋅222

Divide 1 by 1.

x=±22⋅2

x=±22⋅2

Evaluate the exponent.

x=±22⋅2

x=±22⋅2

x=±22⋅2

Multiply 2 by 2.

x=±24

x=±24

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

x=24

Next, use the negative value of the ± to find the second solution.

x=-24

The complete solution is the result of both the positive and negative portions of the solution.

x=24,-24

x=24,-24

x=24,-24

The result can be shown in multiple forms.

Exact Form:

x=24,-24

Decimal Form:

x=0.35355339…,-0.35355339…

Solve Using the Square Root Property (( square root of 5)/2)^2=((3( square root of 2))/4)^2+x^2