Solve for x, x^2-5x+3
Solve for y, y=x^2+4x+16
There is no equation given if you just write down an expression. An equation would have an equals (=) sign. Please provide the full equation so that it can be solved.
I assume that you meant:
solve for x, x^2 + 4x + 16 = 0
using completing the square, ....
x^2 + 4 x + .... = -16 + ....
x^2 + 4 x + 4 = -16 + 4
(x + 2)^2 = -12
x + 2 = ± √-12 = ± 2√3 i
x = -2 ± 2√3 i , which of course is a complex number
Yes, that is correct!
The solutions for x are imaginary since the expression inside the square root is negative.
Well done!
To solve the equation x^2 - 5x + 3 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = -5, and c = 3.
Substituting the values into the quadratic formula:
x = (5 ± √((-5)^2 - 4(1)(3))) / (2(1))
Simplifying further:
x = (5 ± √(25 - 12)) / 2
x = (5 ± √13) / 2
So, the solutions for x are:
x = (5 + √13) / 2
and
x = (5 - √13) / 2
To solve the quadratic equation x^2 - 5x + 3 = 0, you can use the quadratic formula, which is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the quadratic equation. For our given equation x^2 - 5x + 3 = 0, we can identify:
a = 1
b = -5
c = 3
Now, plug these values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4*1*3)) / (2*1)
Simplifying further:
x = (5 ± √(25 - 12)) / 2
x = (5 ± √13) / 2
Therefore, the two possible solutions for x are:
x = (5 + √13) / 2 and x = (5 - √13) / 2