How do you solve x² + 3x - 10 = 0?

To solve the quadratic equation x² + 3x - 10 = 0, you can use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / 2a

In this equation, a, b, and c are the coefficients from the standard form ax² + bx + c = 0. For your equation:

• a = 1
• b = 3
• c = -10

Step 1: Calculate the Discriminant

The discriminant is given by b² - 4ac. Plugging in the values:

3² - 4(1)(-10) = 9 + 40 = 49

Step 2: Apply the Quadratic Formula

Now substitute the values into the quadratic formula:

x = (-3 ± √49) / (2 * 1)

Step 3: Simplify

Since the square root of 49 is 7, we have:

x = (-3 ± 7) / 2

Step 4: Find the Two Solutions

• x₁ = (-3 + 7) / 2 = 4 / 2 = 2
• x₂ = (-3 - 7) / 2 = -10 / 2 = -5

The solutions to the equation x² + 3x - 10 = 0 are x = 2 and x = -5.