Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

mc048-1.jpg

a
3.56, –0.56
b
–3.56, –0.56
c
3.56, 0.56
d
–3.56, 0.56

Answer 1

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 6.84, and c = -5.98. Plugging these values into the quadratic formula, we get:

x = (-(6.84) ± √((6.84)^2 - 4(1)(-5.98))) / (2(1))

Simplifying further:

x = (-6.84 ± √(46.9056 + 23.92)) / 2

x = (-6.84 ± √70.8256) / 2

Now, let's find the two possible solutions:

x₁ = (-6.84 + √70.8256) / 2
x₁ = (-6.84 + 8.4247) / 2
x₁ = 1.5847 / 2
x₁ = 0.79 (rounded to the nearest hundredth)

x₂ = (-6.84 - √70.8256) / 2
x₂ = (-6.84 - 8.4247) / 2
x₂ = -15.2647 / 2
x₂ = -7.63 (rounded to the nearest hundredth)

Therefore, the solutions to the equation are 0.79 and -7.63.