How do you solve $\sqrt{x^{2} + 5} = x + 3$ $sqrt(x^2+5)=x+3$ ?

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Answer 1 · 2016-07-14T01:27:58

Square both sides of the equation.

${(\sqrt{x^{2} + 5})}^{2} = {(x + 3)}^{2}$ $(sqrt(x^2 + 5))^2 = (x + 3)^2$

$x^{2} + 5 = x^{2} + 6 x + 9$ $x^2 + 5 = x^2 + 6x + 9$

$x^{2} - x^{2} - 6 x + 5 - 9 = 0$ $x^2 - x^2 - 6x + 5 - 9 = 0$

$- 6 x = 4$ $-6x = 4$

$x = - \frac{2}{3}$ $x = -2/3$

Checking in the original equation, we find this solution works. Hence, the solution set is ${- \frac{2}{3}}$ ${-2/3}$ .

Hopefully this helps!

How do you solve √x2+5=x+3sqrt(x^2+5)=x+3?