# How do you solve the equation and identify any extraneous solutions for x=sqrt(-7x+8)?

${x}^{2} = - 7 x + 8$
${x}^{2} + 7 x - 8 = 0$
${x}_{1 , 2} = \frac{- 7 \pm \sqrt{49 + 32}}{2} = \frac{- 7 \pm \sqrt{81}}{2}$
${x}_{1} = \frac{- 7 - 9}{2} = - 8$
${x}_{2} = \frac{- 7 + 9}{2} = 1$
substituting back into our original expression we see that only ${x}_{2} = 1$ can be used.