Question

Solve the equation 5, x, squared, minus, 10, x, minus, 12, equals, 05x
2
−10x−12=0 to the nearest tenth.

Answer 1

To solve the equation \( 5x^2 - 10x - 12 = 0 \), we can use the quadratic formula, which is given by:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

In this case, the coefficients are:
- \( a = 5 \)
- \( b = -10 \)
- \( c = -12 \)

First, we need to calculate the discriminant \( b^2 - 4ac \):

\[
b^2 = (-10)^2 = 100
\]

\[
4ac = 4 \cdot 5 \cdot (-12) = -240
\]

Now, we can calculate the discriminant:

\[
b^2 - 4ac = 100 - (-240) = 100 + 240 = 340
\]

Next, we substitute \( a \), \( b \), and the discriminant into the quadratic formula:

\[
x = \frac{-(-10) \pm \sqrt{340}}{2 \cdot 5}
\]

This simplifies to:

\[
x = \frac{10 \pm \sqrt{340}}{10}
\]

Now, we calculate \( \sqrt{340} \):

\[
\sqrt{340} \approx 18.437 \quad (\text{to approximate for the calculation})
\]

Now we substitute back into the equation:

\[
x = \frac{10 \pm 18.437}{10}
\]

This gives us two possible solutions:

1.

\[
x = \frac{10 + 18.437}{10} = \frac{28.437}{10} \approx 2.8437
\]

2.

\[
x = \frac{10 - 18.437}{10} = \frac{-8.437}{10} \approx -0.8437
\]

Now, we round these values to the nearest tenth:

1. \( x \approx 2.8 \)
2. \( x \approx -0.8 \)

Thus, the solutions to the equation \( 5x^2 - 10x - 12 = 0 \) to the nearest tenth are:

\[
\boxed{2.8} \quad \text{and} \quad \boxed{-0.8}
\]