Will you please check my work?
I'm supposed to "Use square roots to solve the following equations; round to the nearest hundredth, if necessary."
1. 5x^2 - 526 = -651
My Work:
5x^2 - 526 + 526 = -651 + 526
(sq root of) 5x^2 = (sq root of) -125 = 5x/5 = 11.18033989/5 = 2.24
2. 3z^2 - 22 = 56
My Work:
3z^2 - 22 + 22 = 56 + 22 =
(sq root of)3z^2 = (sq root of)78 = 3z/3 = 8.831760866 = 2.94
Did I do these correctly? Also, (as dumb as it seems) I sometimes have trouble rounding, so can you make sure I did that correctly, as well?
Thanks so much!
Note: this is a corrected version of a question I asked before.
1. 5x^2 - 526 = -651
My Work:
5x^2 - 526 + 526 = -651 + 526
(sq root of) 5x^2 = (sq root of) -125 = 5x/5 = 11.18033989/5 = 2.24
-----------------------------
The square root of a negative number is imaginary, not a real number
anyway
5 x^2 = -125
x^2 = -25
x = 5 i
2. 3z^2 - 22 = 56
My Work:
3z^2 - 22 + 22 = 56 + 22 =
(sq root of)3z^2 = (sq root of)78 = 3z/3 = 8.831760866 = 2.94
----------------------------
3 z^2 = 78
z^2 = 26
z = sqrt(26) = 5.10
Let's go through your work step by step and check if it is correct:
1. 5x^2 - 526 = -651
To solve this equation using square roots, you need to isolate the variable x. Here's your work:
5x^2 - 526 + 526 = -651 + 526
(sq root of) 5x^2 = (sq root of) -125 = 5x/5 = 11.18033989/5 = 2.24
Your work contains some errors. Let's correct them:
5x^2 - 526 + 526 = -651 + 526
5x^2 = -125
At this point, we can't take the square root of a negative number since it would involve imaginary numbers. It seems that there might be no real solutions for this equation.
2. 3z^2 - 22 = 56
Your work:
3z^2 - 22 + 22 = 56 + 22 =
(sq root of)3z^2 = (sq root of)78 = 3z/3 = 8.831760866 = 2.94
Let's correct your work:
3z^2 - 22 + 22 = 56 + 22
3z^2 = 78
Now we can take the square root:
(sq root of)3z^2 = (sq root of)78
To solve for z, we need to take both the positive and negative square roots:
z = ±(sq root of)78
Calculating the square root of 78 results in approximately ±8.831760867.
Now, let's address the rounding:
In the first problem, since there was no real solution, rounding is not applicable.
In the second problem, the solution is ±8.831760867. To round to the nearest hundredth, you need to keep only two decimal places. Therefore, the rounded answer is ±8.83.
So to summarize, the corrected solutions for the equations are:
1. No real solutions.
2. z = ±8.83
Make sure to double-check your work, especially when dealing with square roots and rounding.