Question

√2x^2-3x-2√2=0 solve by completing the square

Answer 1

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Answer 2

Answer:

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

$x^2-\frac{3}{\sqrt{2}}x-2=0$

$x^2-\frac{3}{\sqrt{2}}x=2$

$x^2-\frac{3}{\sqrt{2}}x+(\frac{3}{2\sqrt{2}})^2=2+(\frac{3}{2\sqrt{2}})^2$

$(x-\frac{3}{2\sqrt{2}})^2=2+\frac{9}{4\times2}$

$(x-\frac{3}{2\sqrt{2}})^2=\frac{16+9}{8}$

$(x-\frac{3}{2\sqrt{2}})^2=\frac{25}{8}$

$x-\frac{3}{2\sqrt{2}}=\pm\sqrt{\frac{25}{8}}$

$x-\frac{3}{2\sqrt{2}}=\pm\frac{5}{2\sqrt{2}}$

$x-\frac{3}{2\sqrt{2}}=\frac{5}{2\sqrt{2}}\:\:and\:\:x-\frac{3}{2\sqrt{2}}=-\frac{5}{2\sqrt{2}}$

$x=\frac{5}{2\sqrt{2}}+\frac{3}{2\sqrt{2}}\:\:and\:\:x-\frac{3}{2\sqrt{2}}=-\frac{5}{2\sqrt{2}}+\frac{3}{2\sqrt{2}}$

$x=\frac{8}{2\sqrt{2}}\:\:and\:\:x=\frac{-2}{2\sqrt{2}}$

$x=\sqrt{8}\:\:and\:\:x=\frac{-1}{\sqrt{2}}$

Therefore, Value of x is 8 and -1/√2.