1. solve the equation: (x-4)^2 -28 = 8 show your work. don’t forget that you will get two answers. 2. this is josh’s solution for the equation : step 1: x² - 6x – 7 = 0 step 2: x² - 6x = 7 step 3: x² - 6x + 9 = 7 + 9 step 4: (x – 3)² = 16 step 5: x – 3 = 16 step 6: x = 19 step 7: x – 3 = -16 step 8: x = -13 where did josh make his mistake? what are the solutions to this equation? show all of your work. this problem is solved using completing the square. the mistake was in step here is how to correctly solve the equation: 3. use the quadratic formula to solve x^2 - 4x + 3 show your work.

1.
(x-4)^2 -28 = 8
(x-4)^2 = 8 + 28 = 36
(x-4) = +/-6
x =  6 + 4 or -6 + 4
x = 10 or -2

2.
Mistake in Step 5: x – 3 = 16
Step 4: (x – 3)² = 16
Step 5: (x – 3) = +/-4
Step 6: x = 4 + 3 or -4 + 3
Step 7: x = 7 or -1

3.
x^2 - 4x + 3 = 0
quadratic eqn x = [-b +/- sqrt(b^2-4ac)]/2a
where in this case
a = 1, b = -4, c = 3
x =  [-(-4) +/- sqrt((-4)^2-4*1*3)]/2*1
= [4 +/- sqrt(16 - 12)]/2
= [4 +/- sqrt(4)]/2
= [4 +/- 2]/2
= 6/2 or 2/2
= 3 or 1

Hello there!

(x - 4)² - 28 = 8

x² - 8x - 12 = 8

Subtract 8 from both sides

x² - 8x - 12 - 8 = 8 - 8

x² - 8x - 20 = 0

Now we need to factorize the left side

(x + 2)(x - 10) = 0

Then set factors equal to 0

x + 2 = 0 or x - 10 = 0

x = 0 - 2 or x = 0 + 10

x = -2 or x = 10

Thus,

The answer is x = -2 or x = 10



Where did Josh made his mistake?

I don't know what was wrong with Josh, but he didn't even try to solve the equation correctly. I can't even think where in the world he got that first step.



What are the solutions to this equation?

The solution to this equation is x = -2 or x = 10



#3 Use the quadratic formula to solve:

x² - 4x + 3

We cannot simplify this, since there is no like terms. For that reason, there is no need to use the quadratic formula. However, we can factorize it :)

The factor is: (x - 1)(x - 3)



I hope the steps are clear for you to understand. If you have any questions about the answer, just let know.

As always, it is my pleasure to help students like you :)