√2x2-3x-2√2=0 by completing the square
Answers
Answer:
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Step-by-step explanation:
Value of x is 8 and -1/√2.
Step-by-step explanation:
Given Quadratic Equation,
√2 x² - 3x - 2√2 = 0
To find: Value of x
x^2-\frac{3}{\sqrt{2}}x-2=0x
2
−
2
3
x−2=0
x^2-\frac{3}{\sqrt{2}}x=2x
2
−
2
3
x=2
x^2-\frac{3}{\sqrt{2}}x+(\frac{3}{2\sqrt{2}})^2=2+(\frac{3}{2\sqrt{2}})^2x
2
−
2
3
x+(
2
2
3
)
2
=2+(
2
2
3
)
2
(x-\frac{3}{2\sqrt{2}})^2=2+\frac{9}{4\times2}(x−
2
2
3
)
2
=2+
4×2
9
(x-\frac{3}{2\sqrt{2}})^2=\frac{16+9}{8}(x−
2
2
3
)
2
=
8
16+9
(x-\frac{3}{2\sqrt{2}})^2=\frac{25}{8}(x−
2
2
3
)
2
=
8
25
x-\frac{3}{2\sqrt{2}}=\pm\sqrt{\frac{25}{8}}x−
2
2
3
=±
8
25
x-\frac{3}{2\sqrt{2}}=\pm\frac{5}{2\sqrt{2}}x−
2
2
3
=±
2
2
5
x-\frac{3}{2\sqrt{2}}=\frac{5}{2\sqrt{2}}\:\:and\:\:x-\frac{3}{2\sqrt{2}}=-\frac{5}{2\sqrt{2}}x−
2
2
3
=
2
2
5
andx−
2
2
3
=−
2
2
5
x=\frac{5}{2\sqrt{2}}+\frac{3}{2\sqrt{2}}\:\:and\:\:x-\frac{3}{2\sqrt{2}}=-\frac{5}{2\sqrt{2}}+\frac{3}{2\sqrt{2}}x=
2
2
5
+
2
2
3
andx−
2
2
3
=−
2
2
5
+
2
2
3
x=\frac{8}{2\sqrt{2}}\:\:and\:\:x=\frac{-2}{2\sqrt{2}}x=
2
2
8
andx=
2
2
−2
x=\sqrt{8}\:\:and\:\:x=\frac{-1}{\sqrt{2}}x=
8
andx=
2
−1
Therefore, Value of x is 8 and -1/√2.