Question

Solve the equation 25z2 + 140 = −29 by using square roots.

A. z = ±13/5
B. z = ±29/5
C. no real solutions
D. z = ±7/5

Answer 1

Option C, no real solutions

Explanation:

Step 1: Subtract 140 from both sides

`25z^2 + 140 = -29`

`25z^2 + 140 -140 = -29 -140`

`25z^2 = -169`

Step 2: Divide both sides by 25

`(25z^2)/(25) = (-169)/(25)`

`z^2 = -6.76`

Step 3: Square root both sides

`√(z^2) = √(-6.76)`

Since we are trying to square root a negative it would cause imaginary solutions so in conclusion we have no real solutions.

Answer: Option C, no real solutions