Question 119766: Solve using the quadratic formula please:
x^2-3x-23=5
Please provide step by step instructions to help me understand.
Thanks!
C
Answer by Caallen2(9)   (Show Source):
You can put this solution on YOUR website! This too is solved like the previous equation you submitted.
To begin you need to make one side equal to zero to get the total equation so you can solve for x.
x^2-3x-23=5
subtract 5 from both sides
x^2 – 3x – 23 – 5 = 5 - 5
Simplify
x^2 – 3x – 28 = 0
Now you will break down this equation into two simpler equations. To do this you must determine which factors are needed. For x the factors are 1, however for -28 the factors are either 1 and 28 or 2 and 14 or 4 and 7. To determine which of these to use you must look to the middle number, which is -3. The factors that would make - 3x would be -7 and 4.
(x - 7)(x + 4)= 0
Start with
x – 7 = 0
add 7 to both sides
x – 7 + 7 = 0 + 7
x = 7
now for the second part
x + 4 = 0
subtract 4 from both sides
x + 4 – 4 = 0 - 4
x = -4
So your solution will be x = 7, x = -4
To check your solution plug one of the answers for x into your original equation and solve.
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