Question

12)Solve each equation or inequality. Write solutions to inequalities in interval notation. If no solution exists, write no solution.

Answer 1

Given:

$x+4=\sqrt{5x+26}$

Required:

We need to solve the given equation

Explanation:

take square both side

$\begin{gathered} (x+4)^2=5x+26 \\ x^2+8x+16=5x=26 \\ x^2+3x-10=0 \end{gathered}$

now use factorization method

$\begin{gathered} x^{2}+3x-10=0 \\ x^2+5x-2x-10=0 \\ (x+5)(x-2)=0 \\ x=-5 \\ and \\ x=2 \end{gathered}$

Final answer:

solution x=-5 and x=2