solve(x-1)^2=-4..... i used the quadratic formula but got stock ... please help thank you
If there is no typo, the solution is complex.
(x-1)^2=-4
=>
(x-1)=±2i
so
x=1±2i
There is no REAL solution.
Since the left side is something squared it must always be positive, and cannot be the value of -4 found on the right side,
or, if you allow complex numbers
x+1 = ± √-4
x = -1 ± 2i
To solve the equation (x-1)^2 = -4, we can use a combination of the quadratic formula and complex numbers.
Let's begin by expanding (x-1)^2 to get rid of the exponent:
(x-1)^2 = (-4)
x^2 - 2x + 1 = -4
Now, rearrange the equation to bring all terms to one side:
x^2 - 2x + 1 + 4 = 0
x^2 - 2x + 5 = 0
Now we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = -2, and c = 5. Plug these values into the quadratic formula:
x = (-(-2) ± √((-2)^2 - 4(1)(5))) / (2(1))
x = (2 ± √(4 - 20)) / 2
x = (2 ± √(-16)) / 2
Here, we encounter a problem because the square root of a negative number is not defined in the real number system. However, we can work with complex numbers to find the solution.
The square root of -16 can be expressed as 4i, where i is the imaginary unit (√(-1)).
So, our equation becomes:
x = (2 ± 4i) / 2
Now, we simplify further:
x = 2/2 ± 4i/2
x = 1 ± 2i
Therefore, the solutions to the equation (x-1)^2 = -4 are x = 1 + 2i and x = 1 - 2i.