Solving quadratic equation By quadratic formula 2m² - 7m - 13 = - 10

We are given the quadratic equation:

\[
2m^2 - 7m - 13 = -10
\]

### Step 1: Bring all terms to one side of the equation.

Add \( 10 \) to both sides to set the equation equal to zero:

\[
2m^2 - 7m - 13 + 10 = 0
\]

Simplifying:

\[
2m^2 - 7m - 3 = 0
\]

### Step 2: Apply the quadratic formula.

The quadratic formula is:

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

In this case, \( a = 2 \), \( b = -7 \), and \( c = -3 \).

### Step 3: Calculate the discriminant.

The discriminant is the part under the square root:

\[
\Delta = b^2 - 4ac
\]

Substitute the values:

\[
\Delta = (-7)^2 - 4(2)(-3) = 49 + 24 = 73
\]

### Step 4: Solve for \( m \).

Now, substitute the discriminant and the values of \( a \) and \( b \) into the quadratic formula:

\[
m = \frac{-(-7) \pm \sqrt{73}}{2(2)}
\]

Simplifying:

\[
m = \frac{7 \pm \sqrt{73}}{4}
\]

### Step 5: Provide the solutions.

The solutions are:

\[
m_1 = \frac{7 + \sqrt{73}}{4}, \quad m_2 = \frac{7 - \sqrt{73}}{4}
\]

These are the two solutions to the quadratic equation.

Would you like to evaluate these numerically or explore further details?

Here are 5 related questions to deepen understanding:
1. How do you determine if the roots of a quadratic equation are real or imaginary?
2. What does the discriminant tell us about the nature of the roots?
3. How does the quadratic formula change for simpler equations like \( ax^2 + bx + c = 0 \)?
4. Can you solve quadratic equations using factoring instead of the quadratic formula?
5. What are some real-life applications of solving quadratic equations?

**Tip:** Always simplify the quadratic equation to standard form \( ax^2 + bx + c = 0 \) before applying the quadratic formula.

Learn how to solve the quadratic equation 2m² - 7m - 13 = -10 using the quadratic formula. Step-by-step solution provided with calculation of discriminant and final solutions. Suitable for high school students.

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