Question

What are the exact solutions of (x² - 5x = 7 = 0), where (x = (-b ± √(b²-4ac))(2a))?

1. (x = 1, -6)
2. (x = 2, -7)
3. (x = 3, -8)
4. (x = 4, -9)

Answer 1

The provided options for the quadratic equation x² - 5x - 7 = 0 do not match the solutions obtained from the quadratic formula, which are x = (5 ± √53) / 2, since √53 is not a perfect square.

Step-by-step explanation:

The exact solutions for a quadratic equation in the form of ax² + bx + c = 0 can be found using the quadratic formula, which is x = (-b ± √(b²-4ac)) / (2a). The original equation provided appears to be a typographical error, so we will proceed with finding the solutions to the quadratic equation x² - 5x - 7 = 0, which seems to be the equation intended based on the provided answer options.

To find the solutions, we substitute a = 1, b = -5, and c = -7 into the quadratic formula:

x = (-(-5) ± √((-5)² - 4(1)(-7))) / (2(1))
x = (5 ± √(25 + 28)) / 2
x = (5 ± √53) / 2

Since √53 is not a perfect square, we cannot simplify this any further to get exact whole number solutions. Hence, the original answer options provided do not correspond to this particular equation.