Solve for the variable:3(2y+7)^ 2=27
Multiply (2y+7)(2y+7)
It is fine to divide both sides by 3 first, that will make the numbers a little smaller.
You will have (2y+7)(2y+7) = 27
After multiplying, you should have 3 terms = 27.
Subtract the 27 from both sides so that you will have a trinomial = 0. You can then factor to find two different values for x.
Are you okay from here?
To solve for the variable in the equation 3(2y+7)^2 = 27, we can follow these steps:
1. Begin by isolating the squared term on one side of the equation. Divide both sides of the equation by 3:
(2y+7)^2 = 27 / 3
Simplifying the right side gives us:
(2y+7)^2 = 9
2. Take the square root of both sides of the equation to eliminate the squared term:
√((2y+7)^2) = ±√9
Simplifying the right side gives us:
2y + 7 = ±3
3. Now we will solve for y by subtracting 7 from both sides:
2y = ±3 - 7
Simplifying the right side gives us:
2y = -4 or 2y = -10
4. Finally, divide both sides by 2 to isolate y:
y = -4 / 2 or y = -10 / 2
Simplifying gives us the two solutions:
y = -2 or y = -5
Therefore, the solutions to the equation 3(2y+7)^2 = 27 are y = -2 and y = -5.