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 - 256 = -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!
I wrote the first problem incorrectly. It's supposed to be 5x^2 - 526 = -651
I apologize.
5x^2 - 526 = -651
5x^2 = -125
x^2 = -25
Unless you have another typo, there is no real number solution, since we cannot take the square root of a negative.
If you equation was supposed to be
5x^2 - 526x= -651
5x^2 - 526x + 651 = 0
x = (526 ± √263656)/10
= appr 103.95 or appr 1.25
2nd:
3z^2- 22 = 56
3z^2 = 78
z^2 = 26
z ± √26 = ± 5.09901..= appr ±5.10
To solve the equations using square roots, you need to follow a slightly different approach. Let's go through each equation step by step:
1. 5x^2 - 256 = -651
To solve this equation, first, isolate the variable term by adding 256 to both sides:
5x^2 = -651 + 256
5x^2 = -395
Now, divide both sides of the equation by 5:
x^2 = -395/5
x^2 = -79
Since we cannot take the square root of a negative number using real numbers, this equation has no real solutions. Therefore, there is no need to continue with the calculations.
2. 3z^2 - 22 = 56
Similarly, let's isolate the variable term by adding 22 to both sides:
3z^2 = 56 + 22
3z^2 = 78
Now, divide both sides of the equation by 3:
z^2 = 78/3
z^2 = 26
To find the value of z, we can take the square root of both sides:
√(z^2) = √(26)
Remember that when taking the square root of a positive number, we consider both the positive and negative roots:
z = ±√(26)
Now, if you want to round the answer to the nearest hundredth, approximate the square root of 26:
z ≈ ±5.10
So, the correct solution is z ≈ ±5.10, with the positive and negative indicating two possible solutions.
In summary, you did not solve the first equation correctly because it has no real solutions. However, you correctly solved the second equation, and the rounding was done accurately. Just remember to consider both positive and negative roots when taking the square root.