Answer:
y = 4.71 and y = -8.71
Explanation:
Step 1: Subtract 5 from both sides:
((y + 2)^2 + 5 = 50) - 5
(y + 2)^2 = 45
Step 2: Take the square root of both sides, subtract 2 from both sides, and round to the nearest hundredth to solve for y.
- Remember that taking the square root will give us both a negative and positive answer on the right-hand side of the equation.
- This is because squaring both a positive and negative number gives us. For example 2^2 = 2 * 2 = 4 but (-2)^2 = -2 * -2 = 4 also
Positive answer:
√(y + 2)^2 = √45
(y + 2 = √45) - 2
y = √45 - 2
y = 4.708203932
y = 4.71
Thus, one answer for y (rounded to the nearest hundredth) is approximately 4.71.
Negative answer:
√(y + 2)^2 = -√45
(y + 2 = -√45) - 2
y = -√45 - 2
y = -8.708203932
y ≈ - 8.71
Thus, the other answer for y (rounded to the nearest hundredth) approximately. -8.71
Optional Step 3: We can check our work by plugging in 4.71 and -8.71 for y and seeing whether we get 50. Because they're rounded, you won't get exactly 50, but the answer should be close enough for us to trust our approximations:
Plugging in 4.71 for y:
(4.71 + 2)^2 + 5 = 50
(6.71)^2 + 5 = 50
45.0241 + 5 = 50
50.0241 > 50
Our answer is close enough to 50 that we can trust our approximation.
Plugging in -8.71 for y:
(-8.71 + 2)^2 + 5 = 50
(-6.71)^2 + 5 = 50
45.0241 + 5 = 50
50.0241 > 50
Again, our answer is close enough to 50 that we can trust our approximation.