solve x²+2x-15=0 by completing quadratic formula

To solve the quadratic equation \( x^2 + 2x - 15 = 0 \) using the quadratic formula, follow these steps:

The quadratic formula is given by:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

For the quadratic equation \( ax^2 + bx + c = 0 \):
- \( a = 1 \)
- \( b = 2 \)
- \( c = -15 \)

Substitute these values into the quadratic formula:

1. Calculate the discriminant:
\[ b^2 - 4ac = 2^2 - 4(1)(-15) = 4 + 60 = 64 \]

2. Take the square root of the discriminant:
\[ \sqrt{64} = 8 \]

3. Substitute \( b \), the square root of the discriminant, and \( a \) into the formula:
\[ x = \frac{-2 \pm 8}{2(1)} \]

4. Simplify the expression for the two possible values of \( x \):
\[ x = \frac{-2 + 8}{2} = \frac{6}{2} = 3 \]
\[ x = \frac{-2 - 8}{2} = \frac{-10}{2} = -5 \]

Therefore, the solutions to the equation \( x^2 + 2x - 15 = 0 \) are:
\[ x = 3 \]
\[ x = -5 \]

Would you like details or have any questions about this solution?

Here are some related questions:

1. How do you derive the quadratic formula?
2. Can you provide an example where the discriminant is negative?
3. How do you complete the square for the equation \( x^2 + 2x - 15 = 0 \)?
4. What is the geometric interpretation of the solutions to \( x^2 + 2x - 15 = 0 \)?
5. How does the quadratic formula change if the coefficient \( a \) is not 1?

**Tip:** Always check your solutions by substituting them back into the original equation to verify that they satisfy the equation.

Learn how to solve the quadratic equation x² + 2x - 15 = 0 using the quadratic formula with a detailed step-by-step solution. This problem covers key algebraic concepts including the quadratic formula and discriminant. Suitable for students in Grades 9-12.

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