Which equation shows the quadratic formula used correctly to solve 7x² + 9x for x?

To solve the quadratic equation 7x² + 9x = 0 using the quadratic formula, we first need to identify the coefficients in the standard form of a quadratic equation ax² + bx + c = 0. In this case:

• a = 7
• b = 9
• c = 0

The quadratic formula is given by:

x = (-b ± √(b² – 4ac)) / (2a)

Next, we can substitute the values of a, b, and c into the formula:

x = ( -9 ± √(9² - 4 * 7 * 0) ) / (2 * 7)

This simplifies to:

x = ( -9 ± √(81) ) / 14

Since √(81) = 9, we can further simplify:

x = ( -9 ± 9 ) / 14

This gives us two potential solutions:

• x = ( -9 + 9 ) / 14 = 0
• x = ( -9 – 9 ) / 14 = -18 / 14 = -9/7

Thus, the solutions to the equation 7x² + 9x = 0 are x = 0 and x = -9/7, which were found using the quadratic formula correctly.