Find the real solutions of the equation $\sqrt { 2 x + 114 } = x - 5$ .
A) $6 - \sqrt { 5 }$
B) $6 \pm 5 \sqrt { 5 }$
C) $12 \pm 10 \sqrt { 5 }$
D) $5 + 6 \sqrt { 5 }$
E) $10 + \sqrt { 5 }$

Question

Quizplus · Accepted Answer

Squaring both sides of the equation gives $2x+114=x^2-10x+25$, which simplifies to $x^2-12x-89=0$. Factoring gives $(x-11)(x+8)=0$, so the solutions are $x=11$ and $x=-8$.

Find the Real Solutions of the Equation 2x+114=x−5\sqrt { 2 x + 114 } = x - 52x+114​=x−5

Find the Real Solutions of the Equation $\sqrt { 2 x + 114 } = x - 5$