Question 1038537
Problem: 

Solve
<img src = "http://image.prntscr.com/image/e009d1ee557b4b37b101ed2228e3e7dc.png">
=========================================================================================
=========================================================================================
Steps


Step 1) {{{8*sqrt(4z^2-43) = 40}}}


Step 2) {{{(8*sqrt(4z^2-43))/8 = 40/8}}}


Step 3) {{{sqrt(4z^2-43) = 5}}}


Step 4) {{{(sqrt(4z^2-43))^2 = 5^2}}}


Step 5) {{{4z^2-43 = 25}}}


Step 6) {{{4z^2-43+43 = 25+43}}}


Step 7) {{{4z^2 = 68}}}


Step 8) {{{(4z^2)/4 = 68/4}}}


Step 9) {{{z^2 = 17}}}


Step 10) {{{sqrt(z^2) = sqrt(17)}}}


Step 11) {{{abs(z) = sqrt(17)}}}


Step 12) {{{z = sqrt(17)}}} or {{{z = -sqrt(17)}}}


-------------------------------------------------


Justification for each step


Step 1) Original Equation


Step 2) Divide both sides by 8


Step 3) Simplify


Step 4) Square both sides


Step 5) Square the square root to cancel it out; 5^2 = 25


Step 6) Add 43 to each side


Step 7) Simplify


Step 8) Divide both sides by 4 to isolate the z^2 term


Step 9) Simplify


Step 10) Apply the square root to both sides to undo the squaring


Step 11) {{{sqrt(z^2)}}} will turn into {{{abs(z)}}}


Step 12) Break up the absolute value
=========================================================================================
=========================================================================================
Answer: 


The two solutions are {{{z = sqrt(17)}}} or {{{z = -sqrt(17)}}}