How do I go about finding the solutions to the following
x^2-6x+25=0
I know the answer is 3-4i and 3+4i
however, I do not know how to go about finding the these solutions
Thanks :)
x^2 - 6x + 25 = 0
Subtract 25 from both sides:
x^2 - 6x = -25
Add 9 to both sides:
x^2 - 6x + 9 = -16
Factor the left hand side:
(x-3)^2 = -16
Take the square root of both sides:
|x - 3| = 4i
Eliminate the absolute value:
x - 3 = -4i or x - 3 = 4i
Add 3 to both sides:
x = 3 - 4i or x - 3 = 4i
Add 3 to both sides:
x = 3 - 4i or x = 3 + 4i
Oh thank you so much
i forgot that when you that the square root of a negative you get the complex #
You are welcome
To find the solutions to the equation x^2 - 6x + 25 = 0, you can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = -6, and c = 25. Plugging these values into the quadratic formula, we get:
x = (6 ± √((-6)^2 - 4*1*25)) / (2*1)
Simplifying further:
x = (6 ± √(36 - 100)) / 2
x = (6 ± √(-64)) / 2
At this point, we have a square root of a negative number, which indicates that the solutions are complex numbers, specifically involving the imaginary unit "i." To simplify the expression further, we can rewrite √(-64) as √(64) * √(-1), which gives us 8i:
x = (6 ± 8i) / 2
Simplifying:
x = (3 ± 4i)
So, the solutions to the equation x^2 - 6x + 25 = 0 are x = 3 - 4i and x = 3 + 4i.