Answer:
x
2
−4x−5=0
All equations of the form ax
2
+bx+c=0 can be solved using the quadratic formula:
2a
−b±
b
2
−4ac
. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
x
2
−4x−5=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2
−(−4)±
(−4)
2
−4(−5)
Square −4.
x=
2
−(−4)±
16−4(−5)
Multiply −4 times −5.
x=
2
−(−4)±
16+20
Add 16 to 20.
x=
2
−(−4)±
36
Take the square root of 36.
x=
2
−(−4)±6
The opposite of −4 is 4.
x=
2
4±6
Now solve the equation x=
2
4±6
when ± is plus. Add 4 to 6.
x=
2
10
Divide 10 by 2.
x=5
Now solve the equation x=
2
4±6
when ± is minus. Subtract 6 from 4.
x=
2
−2
Divide −2 by 2.
x=−1
The equation is now solved.
x=5
x=−1