16=(w2+6)(6)

Rewrite the equation as (w2+6)(6)=16.

(w2+6)(6)=16

Divide each term in (w2+6)(6)=16 by 6.

(w2+6)(6)6=166

Cancel the common factor of 6.

Cancel the common factor.

(w2+6)⋅66=166

Divide w2+6 by 1.

w2+6=166

w2+6=166

Cancel the common factor of 16 and 6.

Factor 2 out of 16.

w2+6=2(8)6

Cancel the common factors.

Factor 2 out of 6.

w2+6=2⋅82⋅3

Cancel the common factor.

w2+6=2⋅82⋅3

Rewrite the expression.

w2+6=83

w2+6=83

w2+6=83

w2+6=83

Subtract 6 from both sides of the equation.

w2=83-6

To write -6 as a fraction with a common denominator, multiply by 33.

w2=83-6⋅33

Combine -6 and 33.

w2=83+-6⋅33

Combine the numerators over the common denominator.

w2=8-6⋅33

Simplify the numerator.

Multiply -6 by 3.

w2=8-183

Subtract 18 from 8.

w2=-103

w2=-103

Move the negative in front of the fraction.

w2=-103

w2=-103

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

w=±-103

Simplify the right side of the equation.

Rewrite -1 as i2.

w=±i2(103)

Pull terms out from under the radical.

w=±i103

Rewrite 103 as 103.

w=±i(103)

Multiply 103 by 33.

w=±i(103⋅33)

Combine and simplify the denominator.

Multiply 103 and 33.

w=±i(10333)

Raise 3 to the power of 1.

w=±i(10333)

Raise 3 to the power of 1.

w=±i(10333)

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

w=±i(10331+1)

Add 1 and 1.

w=±i(10332)

Rewrite 32 as 3.

Use axn=axn to rewrite 3 as 312.

w=±i(103(312)2)

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

w=±i(103312⋅2)

Combine 12 and 2.

w=±i(103322)

Cancel the common factor of 2.

Cancel the common factor.

w=±i(103322)

Divide 1 by 1.

w=±i(1033)

w=±i(1033)

Evaluate the exponent.

w=±i(1033)

w=±i(1033)

w=±i(1033)

Simplify the numerator.

Combine using the product rule for radicals.

w=±i(10⋅33)

Multiply 10 by 3.

w=±i(303)

w=±i(303)

Combine i and 303.

w=±i303

w=±i303

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.

w=i303

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

w=-i303

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

w=i303,-i303

w=i303,-i303

w=i303,-i303

Solve using the Square Root Property 16=(w^2+6)(6)