Solve the equation using the quadratic formula (if necessary, round your result to three significant digits and decide which number is smaller or larger x value).

2x^2 + x − 7 = 0

I used the quadratic formula and I got -2.13 as a smaller x-value and 1.6 as larger x-value.

I got both answers wrong.

It asked for 3 significant digits, so your answers from the calculation are probably

1.63745... and -2.13745...

So for the accuracy asked for, try
1.64 and -2.14

To solve the quadratic equation 2x^2 + x - 7 = 0 using the quadratic formula, let's first identify the coefficients a, b, and c.

In this case:
a = 2
b = 1
c = -7

The quadratic formula is:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula:

x = (-(1) ± √((1)^2 - 4(2)(-7))) / (2(2))

Simplifying this equation:

x = (-1 ± √(1 + 56)) / 4

x = (-1 ± √57) / 4

This expression represents two different solutions for x. We can calculate each separately.

To find the smaller x-value, we use the negative square root:

x = (-1 - √57) / 4

Using rounded values, we get:

x ≈ -2.130 (rounded to three significant digits)

To find the larger x-value, we use the positive square root:

x = (-1 + √57) / 4

Using rounded values, we get:

x ≈ 1.630 (rounded to three significant digits)

So, based on the quadratic formula, the smaller x-value is approximately -2.130, and the larger x-value is approximately 1.630.