Question

What are the solutions of this quadratic equation?

x^2 - 6x = 58

Substitute the values of a and b to complete the solutions.

Option 1:
a) x = 6 + √64

Option 2:
b) x = 6 - √64

Option 3:
c) x = 7 + √61

Option 4:
d) x = 7 - √61

Answer 1

The quadratic equation x^2 - 6x = 58 can be solved by using the quadratic formula. The solutions are found to be x = 3 + √67 and x = 3 - √67. None of the options given are correct.

Step-by-step explanation:

Let's solve the quadratic equation x^2 - 6x = 58 by first bringing it into the standard quadratic form ax^2 + bx + c = 0. To do this, we subtract 58 from both sides, resulting in x^2 - 6x - 58 = 0.

Now we use the quadratic formula, -b ± √b^2 - 4ac / 2a, to find the solutions. Here, a = 1, b = -6, and c = -58. Plugging these values into the quadratic formula, we get:

x = (-(-6) ± √((-6)^2 - 4(1)(-58))) / (2(1))
x = (6 ± √(36 + 232)) / 2
x = (6 ± √268) / 2
x = (6 ± √(4×67))) / 2
x = (6 ± 2√67) / 2
x = 3 ± √67

Therefore, the solutions of the quadratic equation are x = 3 + √67 and x = 3 - √67, which means none of the provided options are correct.