Answer:
The exact solutions are [tex]\text{x}=4+3\sqrt{5} \ \text{ or } \ \text{x}=4-3\sqrt{5}[/tex]
They approximate to 10.708204 and -2.708204; round these approximations however needed.
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Work Shown
[tex](\text{x}-4)^2+4=49\\\\(\text{x}-4)^2=49-4\\\\(\text{x}-4)^2=45\\\\\text{x}-4=\pm\sqrt{45}\\\\[/tex]
[tex]\text{x}-4=\pm\sqrt{9*5}\\\\\text{x}-4=\pm\sqrt{9}*\sqrt{5}\\\\\text{x}-4=\pm3\sqrt{5}\\\\\text{x}=4\pm3\sqrt{5}\\\\\text{x}=4+3\sqrt{5} \ \text{ or } \ \text{x}=4-3\sqrt{5}\\\\\text{x} \approx 10.708204 \ \text{ or } \ \text{x} \approx -2.708204\\\\[/tex]
