Answer:
Squaring the left side and simplifying results in (x+8)
Squaring the right side and simplifying results in [tex]x-14\sqrt{x-6}+43[/tex]
Step-by-step explanation:
Given equation is:
[tex]\sqrt{x+8} =7-\sqrt{x-6}---(1)[/tex]
Squaring the left side and simplifying results in (x +8)
Squaring the right side and simplifying results in:
[tex]=(7-\sqrt{x-6})^{2}\\\\=49-2(7)(\sqrt{x-6})+(x-6)\\\\=49-6-14\sqrt{x-6}+x\\\\=x+14\sqrt{x-6}+43[/tex]
Use them to solve (1)
[tex]x+8=x-14\sqrt{x-6}+43\\\\14\sqrt{x-6}=35\\\\\sqrt{x-6}=2.5\\\\x-6=6.25\\\\x=0.25[/tex]
