Answer:
x = 9
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex]x=\sqrt{x+7} +5[/tex]
Step 1: Flip the equation.
[tex]\sqrt{x+7} +5=x[/tex]
Step 2: Add -5 to both sides.
[tex]\sqrt{x+7} +5-5=x-5[/tex]
Step 3: Solve Square Root.
[tex]\sqrt{x+7} =x-5[/tex]
[tex]{x+7} =(x-5)^2[/tex] (Square both sides)
[tex]x+7=x^2-10x+25[/tex]
[tex]-x^2+11x-18=0[/tex]
[tex](-x+2)(x-9)=0[/tex] (Factor left side of equation)
[tex]-x+2=0[/tex] or [tex]x-9=0[/tex] (Set factors equal to 0)
x = 2 or x = 9
x = 2 (Doesn't work on the original equation)
x = 9 (Works in the original equation)
Answer:
x = 9
