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Question
Solve the following equation using the formula:
`x^2 - 6 = 2sqrt(2)x`
Solution
`x^2 - 6 = 2sqrt(2)x`
`\implies x^2-2sqrt2x-6=0`
Here a = 1, b = `-2sqrt(2)` and c = − 6
Then `x = (-b +- sqrt(b^2 - 4ac))/(2a)`
= `(-(-2sqrt2) +- sqrt((-2sqrt(2))^2 - 4(1)(-6)))/(2(1))`
= `(2sqrt(2) +- sqrt(32))/2`
= `(2sqrt(2) +- 4sqrt(2))/2`
= `(2sqrt(2) + 4sqrt(2))/2` and `(2sqrt(2) - 4sqrt(2))/2`
= `(6sqrt(2))/2` and `(-2sqrt(2))/2`
= `3sqrt(2)` and `-sqrt(2)`
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