Question

1. solve:

\sqrt{6c + 15} = c + 4
type a response

Explanation:

Step1: Square both sides to eliminate root

$$(\sqrt{6c+15})^2=(c+4)^2$$
$$6c+15=c^2+8c+16$$

Step2: Rearrange to quadratic form

$$c^2+8c+16-6c-15=0$$
$$c^2+2c+1=0$$

Step3: Factor the quadratic

$$(c+1)^2=0$$

Step4: Solve for c

$$c+1=0$$
$$c=-1$$

Step5: Verify the solution

Substitute $c=-1$ into original equation:
Left side: $\sqrt{6(-1)+15}=\sqrt{9}=3$
Right side: $-1+4=3$
Both sides are equal, so the solution is valid.

Answer:

$c=-1$