Answer:
[tex]x=\frac{25}{36}[/tex]
Step-by-step explanation:
Raise both sides to the power of two:
[tex](\sqrt{x+4}) ^{2}=(3-\sqrt{x}) ^{2} \\x+4=(3-\sqrt{x}) ^{2}[/tex]
Expand the right side:
[tex]x+4=9-6\sqrt{x} +x[/tex]
subtract x from both sides:
[tex]4=9-6\sqrt{x}[/tex]
add [tex]6\sqrt{x}[/tex] to both sides:
[tex]4+6\sqrt{x}=9[/tex]
Subtract 4 from both sides:
[tex]6\sqrt{x}=5[/tex]
Divide both sides by 6:
[tex]\sqrt{x}=\frac{5}{6}[/tex]
Finally. raise both sides to the power of two:
[tex]x=(\frac{5}{6}) ^{2} =\frac{25}{36}[/tex]
