Answer: To solve the quadratic equation 3x^2 - 9 = 7x using the quadratic formula, we first need to rewrite the equation in standard form (ax^2 + bx + c = 0):
3x^2 - 7x - 9 = 0
Now, we can use the quadratic formula to find the solutions for x:
The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 3, b = -7, and c = -9.
Let's plug in these values and calculate the solutions:
x = (7 ± √((-7)^2 - 4 * 3 * -9)) / (2 * 3)
x = (7 ± √(49 + 108)) / 6
x = (7 ± √157) / 6
Now, let's calculate the two possible solutions for x:
x = (7 + √157) / 6 ≈ 2.64 (rounded to the nearest hundredth)
x = (7 - √157) / 6 ≈ -0.97 (rounded to the nearest hundredth)
So, the two solutions to the equation 3x^2 - 9 = 7x are approximately x ≈ 2.64 and x ≈ -0.97 when rounded to the nearest hundredth.