Question

Use the Quadratic Formula to solve the equation. (Enter your answers as a comma-separated list.)5x^2 + x = −5

Answer 1

5x^2 + x = -5

Equal to zero:

5x^2 + x + 5 = 0

General form:

ax^2 + bx + c

Where:

a= 5

b= 1

c= 5

Apply the quadratic formula:

$\frac{-b\pm\sqrt{b^2-4\times a\times c}}{2\times a}$

Replacing:

$\frac{-1\pm\sqrt{1^2-4\times5\times5}}{2\times5}$$\frac{-1\pm\sqrt{-99}}{10}$$\frac{-1\pm\sqrt[\placeholder{⬚}]{-1}\times\sqrt{99}}{10}$$\frac{-1\pm3\sqrt[\placeholder{⬚}]{11}\text{ i}}{10}$

Positive:

$\frac{-1+3i\sqrt[\placeholder{⬚}]{11}}{10}$

Negative

$\frac{-1-3i\sqrt[\placeholder{⬚}]{11}}{10}$