Given (x - 1)² = 50, select the values of x.

Solution:

(x - 1)² = 50

x² - 2x + 1 = 50

x² - 2x - 49 = 0

The above equation is a quadratic equation of the form ax² + bx + c = 0 the roots of which are given by the formula:

\(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

Hence the roots are:

\(\frac{-(-2)\pm \sqrt{(-2)^{2}-4(1)(-49)}}{2(1)}\)

= \(\frac{2\pm \sqrt{4 + 196}{2(1)}\)

= \(\frac{2\pm \sqrt{200}}{2}\)

= \(\frac{2\pm 10\sqrt{2}}{2}\)

= \(\frac{1\pm 5\sqrt{2}}{1}\)

= 1 ± 5√2

The roots are 1 ± 5√2.

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Given (x - 1)² = 50, select the values of x.

Summary:

Given (x - 1)² = 50, select the values of x are 1 ± 5√2.