How do you solve this? 3√2(b√2+5)-2b+√18=0

Expert Answers

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You should keep the term `3sqrt(2(bsqrt2 + 5)) `  to the left side and you need to move the terms -2b and `sqrt18`  to the right side, such that:

`3sqrt(2(bsqrt2 + 5)) = 2b - sqrt18`

You should raise to square both sides, such that:

`9(2(bsqrt2 + 5)) = (2b - sqrt18)^2`

You should notice that `sqrt18 = 3sqrt2` , hence, you may substitute `3sqrt2`  for `sqrt18` , such that:

`18(bsqrt2 + 5) = 4b^2 - 12bsqrt2 + 18`

Opening the brackets, yields:

`18bsqrt2 + 90 = 4b^2 - 12bsqrt2 + 18`

`4b^2 - 12bsqrt2 + 18 - 18bsqrt2- 90 = 0`

`4b^2 - 30bsqrt2 - 72 = 0`

You should divide by 2 such that:

`2b^2 - 15bsqrt2 - 36 = 0`

You should use quadratic formula such that:

`b_(1,2) = (15+-sqrt(225 + 288))/4`

`b_(1,2) = (15+-3sqrt57)/4`

Hence, evaluating the solutions to the given equation yields `b_(1,2) = (15+-3sqrt57)/4` .

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