Question

x^2-13x+42=0

Answer 1

To solve the quadratic equation x^2 - 13x + 42 = 0, we can factorize it or use the quadratic formula.

Method 1: Factoring
To find the factors of 42 that add up to -13, we look for two numbers whose product is 42 and whose sum is -13. These numbers are -6 and -7.

Therefore, the quadratic equation can be factored as follows:
(x - 6)(x - 7) = 0

Setting each factor to zero, we get:
x - 6 = 0 or x - 7 = 0

Solving for x:
x = 6 or x = 7

Hence, the solutions are x = 6 and x = 7.

Method 2: Quadratic Formula
The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solution for x is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 13x + 42 = 0, a = 1, b = -13, and c = 42.

Plugging in these values into the quadratic formula:
x = (-(-13) ± √((-13)^2 - 4(1)(42))) / (2(1))
x = (13 ± √(169 - 168)) / 2
x = (13 ± √1) / 2

Simplifying further:
x = (13 ± 1) / 2
x = 14 / 2 or 12 / 2
x = 7 or 6

Therefore, the solutions are x = 6 and x = 7, which matches the result obtained through factoring.