The equation you provided is:

\[
3x^2 + 2x = 1
\]

Let's solve it step by step.

### Step 1: Rearrange the equation
Move all terms to one side of the equation to set it equal to zero:

\[
3x^2 + 2x - 1 = 0
\]

Now we have a quadratic equation in the form \( ax^2 + bx + c = 0 \), where \( a = 3 \), \( b = 2 \), and \( c = -1 \).

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

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

Substitute \( a = 3 \), \( b = 2 \), and \( c = -1 \) into the formula:

\[
x = \frac{-2 \pm \sqrt{2^2 - 4(3)(-1)}}{2(3)}
\]

### Step 3: Simplify the expression
First, simplify under the square root:

\[
x = \frac{-2 \pm \sqrt{4 + 12}}{6} = \frac{-2 \pm \sqrt{16}}{6}
\]

\[
x = \frac{-2 \pm 4}{6}
\]

### Step 4: Solve for the two possible values of \( x \)
1. \( x_1 = \frac{-2 + 4}{6} = \frac{2}{6} = \frac{1}{3} \)
2. \( x_2 = \frac{-2 - 4}{6} = \frac{-6}{6} = -1 \)

### Final Solution:
The two solutions are:

\[
x = \frac{1}{3} \quad \text{or} \quad x = -1
\]

Let me know if you'd like more details or if you have any questions!

Here are some related questions you might find interesting:
1. How does the discriminant help determine the nature of solutions for a quadratic equation?
2. What is the significance of completing the square in solving quadratic equations?
3. How do we graph the quadratic equation \( 3x^2 + 2x - 1 = 0 \)?
4. What are the practical applications of quadratic equations in real life?
5. How does factoring compare to the quadratic formula in solving quadratics?

**Tip**: Always check the discriminant \((b^2 - 4ac)\) before solving a quadratic equation. It tells you whether the equation has real or complex solutions!

Solve the quadratic equation 3x^2 + 2x - 1 = 0 step-by-step using the quadratic formula. Learn the key algebraic concepts, including the discriminant and how it determines the nature of the roots. This detailed guide is suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation