Question

exam 1 fall25
due sunday by 11:59pm points 100 submitting an external tool available until sep 21 at 11:59pm
exam 1 fall25
score: 50/100 answered: 14/18
question 15
solve for (x): (sqrt{30 - x}=x). if there is no answer write dne.(x =)

Explanation:

Step1: Square both sides

$(\sqrt{30 - x})^2=x^2$, which simplifies to $30 - x=x^2$.

Step2: Rearrange to quadratic form

$x^2+x - 30=0$.

Step3: Factor the quadratic

$(x + 6)(x - 5)=0$.

Step4: Solve for x

Setting each factor equal to zero gives $x+6 = 0$ or $x - 5=0$. So $x=-6$ or $x = 5$.

Step5: Check for extraneous solutions

For $x=-6$, $\sqrt{30-(-6)}=\sqrt{36}=6
eq - 6$.
For $x = 5$, $\sqrt{30 - 5}=\sqrt{25}=5$.

Answer:

$5$