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

Answer:

Option C, no real solutions

Step-by-step 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

$\frac{25z^2}{25} = \frac{-169}{25}$

$z^2 = -6.76$

Step 3:  Square root both sides

$\sqrt{z^2} = \sqrt{-6.76}$

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