What are the solutions to 2*x*2 + 11*x* + 14 = 0?

*x* = –2,  *x* = 2,  *x* = –4, *x* = –7 *x* = 4, *x* = 7

It seems like the equation you're referring to is a quadratic equation of the form:

\[ 2x^2 + 11x + 14 = 0 \]

Let's solve this equation step-by-step.

### Step 1: Identify the coefficients
From the quadratic equation \( 2x^2 + 11x + 14 = 0 \), we can identify the coefficients:
- \( a = 2 \)
- \( b = 11 \)
- \( c = 14 \)

### Step 2: Use the quadratic formula
The quadratic formula is:

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

Substitute \( a = 2 \), \( b = 11 \), and \( c = 14 \) into the formula:

\[
x = \frac{-11 \pm \sqrt{11^2 - 4(2)(14)}}{2(2)}
\]

### Step 3: Simplify the discriminant
\[
b^2 - 4ac = 11^2 - 4(2)(14) = 121 - 112 = 9
\]

### Step 4: Continue solving
Now we can substitute the discriminant back into the quadratic formula:

\[
x = \frac{-11 \pm \sqrt{9}}{4}
\]

Since \( \sqrt{9} = 3 \), we get two possible solutions:

\[
x = \frac{-11 + 3}{4} = \frac{-8}{4} = -2
\]
and
\[
x = \frac{-11 - 3}{4} = \frac{-14}{4} = -\frac{7}{2} = -3.5
\]

### Solutions
The solutions to the equation \( 2x^2 + 11x + 14 = 0 \) are:

\[
x = -2 \quad \text{and} \quad x = -3.5
\]

These solutions do not match all the options you listed. If you have any further clarifications or questions, feel free to ask!

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### Relative Questions:
1. How is the quadratic formula derived?
2. What does the discriminant tell us about the nature of the roots?
3. Can we solve the equation using factoring instead of the quadratic formula?
4. What is the difference between real and complex solutions in quadratic equations?
5. How can we apply the quadratic formula to equations with complex roots?

### Tip:
Always check the discriminant (\(b^2 - 4ac\)) before solving a quadratic equation. If it's positive, you'll have two real solutions; if zero, one real solution; and if negative, two complex solutions.

What are the solutions to 2*x*2 + 11*x* + 14 = 0?

Find the solutions to the quadratic equation 2x² + 11x + 14 = 0 using the quadratic formula. This step-by-step guide covers key algebraic concepts and explains how to apply the quadratic formula to solve for the roots. Perfect for students in Grades 9-12.

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