SOLUTION: Solve http://prntscr.com/bhzilv Justify each step in your solution

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Question 1038537: Solve http://prntscr.com/bhzilv Justify each step in your solution
Found 4 solutions by Othel, josgarithmetic, jim_thompson5910, MathTherapy:
Answer by Othel(27) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is...
8%2Asqrt%284%2Az%5E2-43%29=40
We can begin by dividing both sides by 8...
sqrt%284%2Az%5E2-43%29=5
and now we square both sides...
4%2Az%5E2-43=25
Add 43 to both sides...
4%2Az%5E2=68
Divide by 4...
z%5E2=17
And take the square root...
z=0%2B-sqrt%2817%29
Pay no attention to the zero in the equation, I couldn't represent the positive and negative of the solution without it. It is meaningless to the solution.
Check your answer! Plug it into the original equation!
I hope this helps! Learn on

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Given Equation:
8sqrt%284z%5E2-43%29=40

I will give REASONS for the steps, and you can supply the actual steps.

Multiplicative Inverse and Multiplication Property of Equality;
Meaning of and Property of Square Roots;
Addition Property of Equality;
Multiplication Property of Equality;
Meaning of Squares or Square Roots----depending on what the value is on the side with the value.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Problem:
Solve

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Steps

Step 1) 8%2Asqrt%284z%5E2-43%29+=+40

Step 2) %288%2Asqrt%284z%5E2-43%29%29%2F8+=+40%2F8

Step 3) sqrt%284z%5E2-43%29+=+5

Step 4) %28sqrt%284z%5E2-43%29%29%5E2+=+5%5E2

Step 5) 4z%5E2-43+=+25

Step 6) 4z%5E2-43%2B43+=+25%2B43

Step 7) 4z%5E2+=+68

Step 8) %284z%5E2%29%2F4+=+68%2F4

Step 9) z%5E2+=+17

Step 10) sqrt%28z%5E2%29+=+sqrt%2817%29

Step 11) abs%28z%29+=+sqrt%2817%29

Step 12) z+=+sqrt%2817%29 or z+=+-sqrt%2817%29

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

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%28z%5E2%29 will turn into abs%28z%29

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

The two solutions are z+=+sqrt%2817%29 or z+=+-sqrt%2817%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve http://prntscr.com/bhzilv Justify each step in your solution
8sqrt%284%2Az%5E2+-+43%29+=+40

sqrt%284%2Az%5E2+-+43%29+=+5 -------- Dividing each side by 8

%28sqrt%284z%5E2+-+43%29%29%5E2+=+5%5E2 ---- Squaring each side

4z%5E2+-+43+=+25

4z%5E2+=+68 ------- Adding 43 to both sides

z%5E2+=+68%2F4

z%5E2+=+17

highlight_green%28z+=+%22+%22%2B-+sqrt%2817%29%29