Question

Solve for the roots in simplest form using the quadratic formula:
3x²+42x=-171

Answer 1

To solve the quadratic equation 3x² + 42x = -171 in simplest form using the quadratic formula, we need to rearrange the equation and apply the formula. The roots are approximately 3.29 and -17.46.

Step-by-step explanation:

To solve the quadratic equation 3x² + 42x = -171 using the quadratic formula, we need to rearrange the equation in the form ax² + bx + c = 0, where a = 3, b = 42, and c = 171. Plugging these values into the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

we can calculate the roots. Substituting the values, we get:

x = (-42 ± √(42² - 4 * 3 * -171)) / (2 * 3)

Simplifying further:

x = (-42 ± √(1764 + 2052)) / 6

x = (-42 ± √3816) / 6

The square root of 3816 is approximately 61.77, so the roots are:

x = (-42 + 61.77) / 6 ≈ 3.29

x = (-42 - 61.77) / 6 ≈ -17.46