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):
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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