Solve for the roots in *simplest form* using the quadratic formula:

2, x, squared, plus, 4, x, equals, 6

2*x*2+4*x*=

6

To solve the quadratic equation \(2x^2 + 4x = 6\) for its roots using the quadratic formula, follow these steps:

### Step 1: Write the equation in standard form
First, move all terms to one side of the equation to get it in the standard form \(ax^2 + bx + c = 0\).

\[
2x^2 + 4x - 6 = 0
\]

Here, \(a = 2\), \(b = 4\), and \(c = -6\).

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

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

Substitute the values of \(a\), \(b\), and \(c\) into the formula:

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(2)(-6)}}{2(2)}
\]

### Step 3: Simplify the expression under the square root
First, calculate the discriminant (\(b^2 - 4ac\)):

\[
b^2 - 4ac = 4^2 - 4(2)(-6) = 16 + 48 = 64
\]

Now, substitute back into the quadratic formula:

\[
x = \frac{-4 \pm \sqrt{64}}{4}
\]

### Step 4: Calculate the square root and solve for \(x\)
The square root of 64 is 8, so:

\[
x = \frac{-4 \pm 8}{4}
\]

This gives us two possible solutions:

1. \(x_1 = \frac{-4 + 8}{4} = \frac{4}{4} = 1\)
2. \(x_2 = \frac{-4 - 8}{4} = \frac{-12}{4} = -3\)

### Step 5: Write the final solution
The roots of the equation are \(x = 1\) and \(x = -3\).

Would you like further details or have any questions?

Here are 5 related questions:

1. How can the discriminant help in determining the nature of the roots?
2. What happens if the discriminant is negative in the quadratic formula?
3. How would you solve the equation if the coefficients were fractions?
4. What are some real-world applications of solving quadratic equations?
5. How does completing the square compare to using the quadratic formula?

**Tip:** Always simplify the equation to standard form before applying the quadratic formula to avoid errors in identifying \(a\), \(b\), and \(c\).

Learn how to solve the quadratic equation 2x^2 + 4x = 6 step-by-step using the quadratic formula. This problem involves understanding quadratic equations, applying the quadratic formula, and calculating roots. Suitable for Grades 7-9 students.

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