Find the roots of the quadratic equation $square root of 2 straight x squared space plus 7 straight x space plus 5 square root of 2 space equals space 0$

square root of 2 straight x squared space plus 7 straight x space plus 5 square root of 2 space equals space 0 or rightwards double arrow square root of 2 straight x squared space plus 5 straight x space plus 2 straight x space plus 5 square root of 2 space equals space 0 rightwards double arrow straight x left parenthesis square root of 2 straight x space plus 5 right parenthesis space plus square root of 2 left parenthesis square root of 2 straight x end root plus 5 right parenthesis space equals space 0 rightwards double arrow space left parenthesis square root of 2 straight x end root space plus 5 right parenthesis left parenthesis straight x plus square root of 2 right parenthesis space equals space 0 rightwards double arrow left parenthesis square root of 2 straight x end root space plus 5 right parenthesis space left parenthesis straight x plus square root of 2 right parenthesis space equals space 0 rightwards double arrow space straight x space plus space square root of 2 space equals space 0 square root of 2 straight x end root space plus 5 space equals space 0 rightwards double arrow space straight x space equals negative square root of 2 straight x space equals negative space fraction numerator 5 over denominator square root of 2 end fraction space equals negative space fraction numerator 5 square root of 2 over denominator 2 end fraction space Hence space roots space are space minus square root of 2 comma space minus fraction numerator 5 square root of 2 over denominator 2 end fraction space

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