Solve the quadratic equation by quadratic formula x²+3x-10=0

To solve the quadratic equation \(x^2 + 3x - 10 = 0\) using the quadratic formula, we'll use the formula:

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

Here, the coefficients are:

- \(a = 1\) (coefficient of \(x^2\))
- \(b = 3\) (coefficient of \(x\))
- \(c = -10\) (constant term)

Substituting these values into the formula:

\[
x = \frac{{-3 \pm \sqrt{{3^2 - 4 \cdot 1 \cdot (-10)}}}}{2 \cdot 1}
\]

Simplify inside the square root:

\[
x = \frac{{-3 \pm \sqrt{{9 + 40}}}}{2}
\]

\[
x = \frac{{-3 \pm \sqrt{49}}}{2}
\]

Since \(\sqrt{49} = 7\), we have:

\[
x = \frac{{-3 \pm 7}}{2}
\]

This gives us two solutions:

1. \(x = \frac{{-3 + 7}}{2} = \frac{4}{2} = 2\)
2. \(x = \frac{{-3 - 7}}{2} = \frac{-10}{2} = -5\)

So, the solutions are:

\[
x = 2 \quad \text{and} \quad x = -5
\]

Would you like details on any of the steps? Here are some related questions:

1. How do you determine the discriminant in the quadratic formula?
2. What are the possible types of solutions for a quadratic equation?
3. How do you factorize a quadratic equation if it's factorable?
4. What are other methods to solve a quadratic equation besides the quadratic formula?
5. Can you graphically interpret the solutions of this equation?

**Tip:** The discriminant (\(b^2 - 4ac\)) can help you determine the nature of the roots: if it's positive, there are two real solutions; if zero, one real solution; and if negative, two complex solutions.

Learn how to solve the quadratic equation x² + 3x - 10 = 0 using the quadratic formula step-by-step. This problem covers key algebraic concepts, including the quadratic formula and discriminant. Suitable for students in Grades 7-9.

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