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

(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
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.
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

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