Find all real solutions of √6x2+2x−√32=0.
√6x2+2x−√32=0Given√6x2+2x=√32Add √32x2+2√6x=√32√6Divide both sides of the equation by √6 to make the coefficient of x2 equal to 1x2+2√6+16=√32√6+16Complete the square: add (2√62)2=16(x+1√6)2=23Perfect square, simplify the right side of the equationx+1√6=±√23Take the square rootx=−1√6±√23Subtract 1√6x=−1√6+√23 and x=−1√6−√23Solve for xx=√66 and x=−√62Simplify
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