1. 4x2 - 25 = 0 by factorization
Answers
Answer:
Step-by-step explanation:
4x
2
−25=0
Quadratic equations like this one, with an x
2
term but no x term, can still be solved using the quadratic formula,
2a
−b±
b
2
−4ac
, once they are put in standard form: ax
2
+bx+c=0.
4x
2
−25=0
This equation is in standard form: ax
2
+bx+c=0. Substitute 4 for a, 0 for b, and −25 for c in the quadratic formula,
2a
−b±
b
2
−4ac
.
x=
2×4
0±
0
2
−4×4(−25)
Square 0.
x=
2×4
0±
−4×4(−25)
Multiply −4 times 4.
x=
2×4
0±
−16(−25)
Multiply −16 times −25.
x=
2×4
0±
400
Take the square root of 400.
x=
2×4
0±20
Multiply 2 times 4.
x=
8
0±20
Now solve the equation x=
8
0±20
when ± is plus. Reduce the fraction
8
20
to lowest terms by extracting and canceling out 4.
x=
2
5
Now solve the equation x=
8
0±20
when ± is minus. Reduce the fraction
8
−20
to lowest terms by extracting and canceling out 4.
x=−
2
5
The equation is now solved.
x=
2
5
x=−
2
5
Step-by-step explanation:
4x=25-2
4x=23
X=23/4
X=5³/4