Question

Solve using the quadratic formula. Approximate answers to the nearest tenth.

Answer 1

`\displaystyle x\approx -1.4\text{ or } 2.9`

Explanation:

We want to solve the equation:

`\displaystyle 2x^2-3x-8=0`

Using the quadratic formula.

The quadratic formula is given by:

`\displaystyle x=(-b\pm√(b^2-4ac))/(2a)`

In this case, a = 2, b = -3, and c = -8. Substitute:

`\displaystyle x=(-(-3)\pm√((-3)^2-4(2)(-8)))/(2(2))`

Evaluate:

`\displaystyle x=(3\pm√(73))/(4)`

So, our solutions are:

`\displaystyle x=(3+√(73))/(4)\approx 2.9\text{ and } x=(3-√(73))/(4)\approx-1.4`