(3t+5)2=7

Take the square root of each side of the equation to set up the solution for t

(3t+5)2⋅12=±7

Remove the perfect root factor 3t+5 under the radical to solve for t.

3t+5=±7

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

3t+5=7

Subtract 5 from both sides of the equation.

3t=7-5

Divide each term by 3 and simplify.

Divide each term in 3t=7-5 by 3.

3t3=73+-53

Cancel the common factor of 3.

Cancel the common factor.

3t3=73+-53

Divide t by 1.

t=73+-53

t=73+-53

Move the negative in front of the fraction.

t=73-53

t=73-53

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

3t+5=-7

Subtract 5 from both sides of the equation.

3t=-7-5

Divide each term by 3 and simplify.

Divide each term in 3t=-7-5 by 3.

3t3=-73+-53

Cancel the common factor of 3.

Cancel the common factor.

3t3=-73+-53

Divide t by 1.

t=-73+-53

t=-73+-53

Simplify each term.

Move the negative in front of the fraction.

t=-73+-53

Move the negative in front of the fraction.

t=-73-53

t=-73-53

t=-73-53

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

t=73-53,-73-53

t=73-53,-73-53

The result can be shown in multiple forms.

Exact Form:

t=73-53,-73-53

Decimal Form:

t=-0.78474956…,-2.54858377…

Solve using the Square Root Property (3t+5)^2=7