Solve x² - 16x + 60 = -12 by completing the steps.

Solution:

Given equation is x² - 16x + 60 = -12

x² - 16x + 60 + 12 = 0

x² - 16x + 72= 0 --- (1)

The above equation is of the form ax² + bx + c and its roots are given by the formula:

Roots of the equation = \(\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)

For equation (1)

b = -16; a = 1; c = 72.

Therefore,

The roots of the equation are:

= \(\frac{-(-16)\pm \sqrt{16^{2}-4(1)(72)}}{2(1)}\)

= \(\frac{16\pm \sqrt{256-288}}{2}\)

= \(\frac{16\pm \sqrt{-32}}{2}\)

= \(\frac{16\pm \sqrt{-(16)(2)}}{2}\)

= \(\frac{16\pm (4)\sqrt{-2}}{2}\)

= \(\frac{16\pm (4i)\sqrt{2}}{2}\)

= \(8\pm i2\sqrt{2}\)

The roots of the equation are 8 + i2√2 and 8 - i2√2

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Solve x² - 16x + 60 = -12 by completing the steps.

Summary:

After completing the steps the roots of the equation are 8 + i2√2 and 8 - i2√2