Q: Solve for x in following equation :
x2 – 3 root 2 + 4 = 0
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Answer:
Answer
Given,
x
2
−3x−4=0
⇒x
2
−3x−4+4=4
⇒x
2
−3x=4
To make a trinomial square on the left side of the equation, We have to find a value that is equal to the square of half of b, the coefficient of x.
So, (
2
b
)
2
=(−
2
3
)
2
Adding the term to both sides of the equation,
x
2
−3x+(−
2
3
)
2
=4+(−
2
3
)
2
⇒x
2
−3x+
4
9
=
4
25
⇒x
2
+2⋅x⋅(−
2
3
)+(−
2
3
)
2
=
4
25
⇒(x−
2
3
)
2
=
4
25
Taking square root of both sides we get,
(x−
2
3
)
2
=±
4
25
⇒x−
2
3
=±
2
5
For
2
5
,x−
2
3
=
2
5
⇒x=
2
5
+
2
3
=4
For −
2
5
,x−
2
3
=−
2
5
⇒x=−
2
5
+
2
3
=−1
Hence, the solution is x=4,−1.
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