Question

Solve for x (x-5) ²+5 =49

Answer 1

Answer:

$\left(x-5\right)^2+5=49$

Subtract 5 from both sides

$\left(x-5\right)^2+5-5=49-5$

$\left(x-5\right)^2=44$

$x-5=\sqrt{44}$

$44=2^{2} \times11$

$x-5=\sqrt{11} \sqrt{2^{2} }$

Radical rule:- $\sqrt[n]{a^{n} } =a$

$x-5=2\sqrt{11}$

Add 5 to both sides

$x=2\sqrt{11}+5$

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$x-5=-2\sqrt{11}$

Add 5 to both sides

$x-5=-2\sqrt{11}$

Ans: $x=2\sqrt{11}+5,\:x=-2\sqrt{11}+5$

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Answer 2

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)