The quadratic formula is a powerful tool that can help us solve quadratic equations of the standard form ax² + bx + c = 0. The formula itself is expressed as:
x = (-b ± √(b² – 4ac)) / (2a)
To use the quadratic formula for the equation 7x² + 9x = 0, we first need to identify the values of a, b, and c from the equation.
- a = 7
- b = 9
- c = 0
Now that we have identified these coefficients, we can substitute them into the quadratic formula:
1. Calculate the discriminant (b² – 4ac):
- Discriminant = 9² – 4(7)(0)
- Discriminant = 81 – 0 = 81
2. Now apply the values to the quadratic formula:
x = (–9 ± √81) / (2 * 7)
3. Calculate the square root of the discriminant:
- √81 = 9
4. Substitute back into the formula:
x = (–9 ± 9) / 14
This gives us two potential solutions:
- x₁ = (–9 + 9) / 14 = 0 / 14 = 0
- x₂ = (–9 – 9) / 14 = -18 / 14 = -9/7
Therefore, the solutions to the equation 7x² + 9x = 0 using the quadratic formula are:
- x = 0
- x = -9/7
By identifying the coefficients and applying the quadratic formula step-by-step, we effectively solved the equation. This method is not only systematic but also leaves no stone unturned in finding both roots of the quadratic equation.