Answer:
[tex]x=2[/tex]
[tex]x=-7[/tex]
Step-by-step explanation:
[tex]\sqrt{9x+63}=x+7[/tex]
Square both sides:-
[tex]9x+63=x^2+14x+49[/tex]
Switch sides:-
[tex]x^2+14x+49=9x+63[/tex]
Subtract 63 from both sides:-
[tex]x^2+14x+49-63=9x+63-63[/tex]
[tex]x^2+14x-14=9x[/tex]
Subtract 9x from both sides:-
[tex]x^2+14x-14-9x=9x-9x[/tex]
[tex]x^2+5x-14=0[/tex]
Now, solve with quadratic formal:-
[tex]x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\times \:1\times \left(-14\right)}}{2\times \:1}[/tex]
[tex]\sqrt{5^2-4\times \:1\times \left(-14\right)}[/tex]
[tex]=\sqrt{5^2+4\times \:1\times \:14}[/tex]
Multiply the numbers :-
[tex]\sqrt{5^2+56}[/tex]
Add :-
[tex]\sqrt{81}[/tex]
Factor numbers:-
[tex]81=9^2[/tex]
[tex]\sqrt{9^2}[/tex]
Radical Rule:-
[tex]\sqrt[n]{a^{n} } =a[/tex]
[tex]\sqrt{9^2}=9[/tex]
[tex]x_{1,\:2}=\frac{-5\pm \:9}{2\times \:1}[/tex]
Separate solutions:-
⇒ [tex]x_1=\frac{-5+9}{2\times \:1}[/tex]
[tex]\frac{4}{2\times \:1}[/tex]
[tex]=\frac{4}{2}[/tex]
→ [tex]=2[/tex]
⇒ [tex]\:x_2=\frac{-5-9}{2\times \:1}[/tex]
[tex]\frac{-5-9}{2\times \:1}[/tex]
[tex]\frac{-14}{2\times \:1}[/tex]
[tex]\frac{-14}{2}[/tex]
→ [tex]=-7[/tex]
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