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Step 1:I'll solve the quadratic equation x^{2} - 4x + 1 = 0 using the quadratic formula.
Step 2:: Identify the coefficients
- $$c = 1
- b = - 4
Step 3:: Recall the quadratic formula
x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}
Step 4:: Substitute the coefficients into the quadratic formula
x = \frac{-(-4) \pm \sqrt{(-4)^{2} - 4(1)(1)}}{2(1)}}
Step 5:: Simplify the calculation
x = \frac{4 \pm 2\sqrt{3}}{2}
x = \frac{4 \pm \sqrt{12}}{2}
Step 6:: Simplify further
x = 2 \pm \sqrt{3}
Final Answer
The solutions are x_{1} = 2 + \sqrt{3} and x_{2} = 2 - \sqrt{3}.
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