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

Math
16=(w2+6)(6)
Rewrite the equation as (w2+6)(6)=16.
(w2+6)(6)=16
Divide each term by 6 and simplify.
Tap for more steps…
Divide each term in (w2+6)(6)=16 by 6.
(w2+6)(6)6=166
Cancel the common factor of 6.
Tap for more steps…
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.
Tap for more steps…
Factor 2 out of 16.
w2+6=2(8)6
Cancel the common factors.
Tap for more steps…
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
Move all terms not containing w to the right side of the equation.
Tap for more steps…
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.
Tap for more steps…
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
The complete solution is the result of both the positive and negative portions of the solution.
Tap for more steps…
Simplify the right side of the equation.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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.
Tap for more steps…
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)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top