5.72 - 7x - 6 = 0 find the roots of the following quadratic equation if they exist
Answers
Answer:
Answer:
The roots are x=\frac{3}{5},-2x=
5
3
,−2
Step-by-step explanation:
Given : Equation 5x^2+7x-6=05x
2
+7x−6=0
To find : The roots of a quadratic equation by completing square method ?
Solution :
Equation 5x^2+7x-6=05x
2
+7x−6=0
Divide both side by 5,
x^2+\frac{7}{5}x-\frac{6}{5}=0x
2
+
5
7
x−
5
6
=0
Applying completing the square,
x^2+\frac{7}{5}x-\frac{6}{5}+(\frac{7}{10})^2-(\frac{7}{10})^2=0x
2
+
5
7
x−
5
6
+(
10
7
)
2
−(
10
7
)
2
=0
(x+\frac{7}{10})^2-\frac{6}{5}-\frac{49}{100}=0(x+
10
7
)
2
−
5
6
−
100
49
=0
(x+\frac{7}{10})^2-\frac{169}{100}=0(x+
10
7
)
2
−
100
169
=0
(x+\frac{7}{10})^2=\frac{169}{100}(x+
10
7
)
2
=
100
169
Taking root both side,
x+\frac{7}{10}=\pm\frac{13}{10}x+
10
7
=±
10
13
Take positive,
x=\frac{13}{10}-\frac{7}{10}x=
10
13
−
10
7
x=\frac{6}{10}x=
10
6
x=\frac{3}{5}x=
5
3
Take negative,
x=-\frac{13}{10}-\frac{7}{10}x=−
10
13
−
10
7
x=\frac{-20}{10}x=
10
−20
x=-2x=−2
Therefore, the roots are x=\frac{3}{5},-2x=
5
3
,