# SOLUTION: 64.) Find all real solutions to each equation. {{{x^2+x+ sqrt(x^2+x)-2=0}}}

Algebra ->  Algebra  -> Test -> SOLUTION: 64.) Find all real solutions to each equation. {{{x^2+x+ sqrt(x^2+x)-2=0}}}      Log On

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 Question 164961This question is from textbook Elementary and Intermediate : 64.) Find all real solutions to each equation. This question is from textbook Elementary and Intermediate Answer by Edwin McCravy(8909)   (Show Source): You can put this solution on YOUR website!``` Put parentheses around the first two terms: Notice that occurs in two places, so let the variable part of the middle term, in this case the whole middle term, be equal to the letter . That is to say we are letting Now we square both sides: So we substitute for in the original equation, and for becomes the much simpler looking equation: Factoring: Using the zero-factor property, So now we have to substitute back. We can tell immediately that has no solution because square roots when written as a radical are never negative, so that square root on the left could not equal to -2 on the right. So we solve Square both sides: Edwin```