Question

Use the quadratic formula to solve for x.

6x²+ 9x= -1
Round your answer to the nearest hundredth.

If there is more than one solution, separate them with commas.
x= ________.

Answer 1

To solve the quadratic equation 6x² + 9x = -1 using the quadratic formula, we can identify the coefficients as follows:

a = 6
b = 9
c = -1

The quadratic formula states that for an equation in the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values from our equation, we have:

x = (-9 ± √(9² - 4(6)(-1))) / (2(6))

Simplifying further:

x = (-9 ± √(81 + 24)) / 12
x = (-9 ± √105) / 12

Using a calculator or simplifying by hand, we can find the approximate solutions:

x ≈ (-9 + √105) / 12 ≈ 0.15
x ≈ (-9 - √105) / 12 ≈ -1.48

Therefore, the solutions to the quadratic equation 6x² + 9x = -1, rounded to the nearest hundredth, are

x ≈ 0.15, x ≈ -1.48.