What are the solutions of the quadratic equation 0 = -x² - 6x - 8?

Solution:

A quadratic equation is an algebraic expression of the second degree in x.

The standard form of a quadratic equation is ax² + bx + c = 0,

where a, b are the coefficients,

x is the variable, and

c is the constant term.

Given, the quadratic equation is 0 = -x² - 6x - 8.

We have to find the solutions of the equation.

Using the quadratic formula,

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

Here, a = -1, b = -6 and c = -8

\(x=\frac{-(-6)\pm \sqrt{(-6)^{2}-4(-1)(-8)}}{2(-1)}\\x=\frac{6\pm \sqrt{36-32}}{-2}\\x=\frac{6\pm \sqrt{4}}{-2}\\x=\frac{6\pm 2}{-2}\)

\(x=\frac{6+2}{-2}=\frac{8}{-2}=-4\)

\(x=\frac{6-2}{-2}=\frac{4}{-2}=-2\)

Therefore, the solutions of the quadratic equation are x = -2 and x = -4.

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What are the solutions of the quadratic equation 0 = -x² - 6x - 8?

Summary:

The solutions of the quadratic equation 0 = -x² - 6x - 8 are x = -2 and x = -4.