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Answer:
x = 5±2 sqrt(11)
Step-by-step explanation:
(x-5) ²+5 =49
Subtract 5 from each side
(x-5) ²+5-5 =49-5
(x-5) ² =44
Take the square root of each side
sqrt((x-5) ²) =±sqrt(44)
sqrt((x-5) ²) =±sqrt(4*11)
x-5 = ±2 sqrt(11)
Add 5 to each side
x-5+5 = 5±2 sqrt(11)
x = 5±2 sqrt(11)
Answer:
[tex]\left(x-5\right)^2+5=49[/tex]
Subtract 5 from both sides
[tex]\left(x-5\right)^2+5-5=49-5[/tex]
[tex]\left(x-5\right)^2=44[/tex]
[tex]x-5=\sqrt{44}[/tex]
[tex]44=2^{2} \times11[/tex]
[tex]x-5=\sqrt{11} \sqrt{2^{2} }[/tex]
Radical rule:- [tex]\sqrt[n]{a^{n} } =a[/tex]
[tex]x-5=2\sqrt{11}[/tex]
Add 5 to both sides
[tex]x=2\sqrt{11}+5[/tex]
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[tex]x-5=-2\sqrt{11}[/tex]
Add 5 to both sides
[tex]x-5=-2\sqrt{11}[/tex]
Ans: [tex]x=2\sqrt{11}+5,\:x=-2\sqrt{11}+5[/tex]
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