Solve....x(x-3)=x-9
x(x-3)=x-9
x-3x=x-9
x=x-6
x=-6
-6(-6-3) =/= -6-9
always check your answer.
x(x-3) = x-9
x^2 - 3x = x - 9
x^2 - 4x + 9 = 0
x = 2 +/- i√5
To solve the equation x(x-3) = x-9, we need to simplify and rearrange the terms to isolate x.
Let's begin by expanding the multiplication on the left side of the equation:
x(x-3) = x-9
x^2 - 3x = x - 9
Now, let's gather all the x terms on one side of the equation by subtracting x from both sides:
x^2 - 3x - x = -9
Simplifying further:
x^2 - 4x = -9
We can now move all terms to one side of the equation to form a quadratic equation equal to zero:
x^2 - 4x + 9 = 0
At this stage, we have a quadratic equation that we can solve using various methods like factoring, completing the square, or using the quadratic formula.
If we attempt to factor the quadratic equation or complete the square, we find that it cannot be factored nicely, and completing the square is quite involved. Therefore, let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, we have a = 1, b = -4, and c = 9. Let's substitute these values into the formula:
x = (-(-4) ± √((-4)^2 - 4(1)(9))) / (2(1))
Simplifying further:
x = (4 ± √(16 - 36)) / 2
x = (4 ± √(-20)) / 2
Here we encounter a problem because the square root of a negative number is not a real number. Therefore, our initial equation has no real solutions.
Hence, the solution to the equation x(x-3) = x-9 is that there are no real solutions.