What are the solutions to 2 x squared minus 8 x minus 42 equals 0?

To solve the quadratic equation:

\[
2x^2 - 8x - 42 = 0
\]

we can follow these steps:

### 1. Divide the entire equation by 2:
This simplifies the equation and makes it easier to solve.

\[
x^2 - 4x - 21 = 0
\]

### 2. Apply the quadratic formula:
The quadratic formula is given by:

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

For the equation \(x^2 - 4x - 21 = 0\), the coefficients are:
- \(a = 1\)
- \(b = -4\)
- \(c = -21\)

Plugging these into the formula:

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-21)}}{2(1)}
\]

\[
x = \frac{4 \pm \sqrt{16 + 84}}{2}
\]

\[
x = \frac{4 \pm \sqrt{100}}{2}
\]

\[
x = \frac{4 \pm 10}{2}
\]

### 3. Solve for the two possible values of \(x\):

\[
x_1 = \frac{4 + 10}{2} = \frac{14}{2} = 7
\]

\[
x_2 = \frac{4 - 10}{2} = \frac{-6}{2} = -3
\]

### Final solutions:
The solutions are \(x = 7\) and \(x = -3\).

Would you like more details on any part of this solution?

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Here are 5 related questions:
1. How do you complete the square for a quadratic equation?
2. Can the quadratic formula be used for non-quadratic equations?
3. What is the discriminant and how does it affect the number of solutions?
4. How do you solve quadratic equations by factoring?
5. What are some real-life applications of quadratic equations?

**Tip:** Always check the discriminant \((b^2 - 4ac)\) before using the quadratic formula to determine the number and type of solutions!

What are the solutions to 2x^2 - 8x - 42 = 0?

Discover how to solve the quadratic equation 2x^2 - 8x - 42 = 0 step-by-step. This solution covers essential algebraic concepts such as simplification and the use of the quadratic formula, ideal for students in Grades 9-10.

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