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x = \frac{\sqrt{5} + 1}{2} \approx 1.618033989
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x≔\frac{\sqrt{5}+1}{2}
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x=\frac{7+5\sqrt{5}+\sqrt{20}}{14}
Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.
x=\frac{7+5\sqrt{5}+2\sqrt{5}}{14}
Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.
x=\frac{7+7\sqrt{5}}{14}
Combine 5\sqrt{5} and 2\sqrt{5} to get 7\sqrt{5}.
x=\frac{1}{2}+\frac{1}{2}\sqrt{5}
Divide each term of 7+7\sqrt{5} by 14 to get \frac{1}{2}+\frac{1}{2}\sqrt{5}.
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