solve using the quadratic formula: x2 – 3x = 2x – 1?

Answer 1

x² - 3x = 2x - 1
x² - 5x + 1 = 0
x = (-b ±√(b²-4ac) ) /2a

x = ( 5 ±√(25 - 4) ) /2a
x = 4.79 or x = 0.2

Answer 2

Well, first we have to make the equation equal to zero. So, by using the change sides change signs method, we would be able to make it equal to zero.

x^2-3x=2x-1
x^2-3x-2x+1=0
x^2-5x+1=0

As you see, I moved 2x and -1 over to the right side of the equation, changing their signs because of the change sides change signs rule. Then I got my second equation. I then added my like terms, -3x-2x, which equals 5x. Then, substituting 5x for -3x-2x, I have a completely simplified quadratic equation equal to zero.
The quadratic formula is as follows:

(-b+/- (sq. root b^2-4ac))/2a. It's makes it easier to follow a formula along with this formula to use it correctly.
ax^2+bx+c=0
Now, our equation is x^2-5x+1=0, so all we have to do is plug in our values in the equation ax^2+bx+c=0 to see what a, b and c equal, then we will be able to use the quadratic formula.
Obviously, a=1 because 1*x^2=x^2. b=-5 when you substitute it into the variable equation, because +-5=-5, and c=1 by substitution into the variable equation.
Therefore our quadratic formula would then be -(-5)+/- (sq. root ((-5)^2-4(1*1))/2(1). We know that -(-5)=5, for one. Also, since we have to follow PEMDAS in the square root of this equation, we first solve the parenthesis. We know that 1*1=1. Also, we know that (-5)^2=25. Then, finally, we know that -4(1)=-4. And, in the denominator, 2(1)=2. Therefore, we have:
(5+/-(sq. root 25-4))/2. We know that 25-4=21. So we then have:
(5+/- (sq. root 21))/2. So, therefore, our two values of x would be:
5+(sq. root 21)/2 and 5- (sq. root 21)/2.
There you go. I'm glad I could help. :)

Answer 3

Get the equation in the form A(x^2) + Bx + C = 0

The quadratic formula is {-b +/- sqrt[(b^2)-4ac]}/2a

So for this equation
x^2 -5x +1 = 0

[5 +/- sqrt(25-4)]/2

[5 +/- sqrt(21)]/2

Answer 4

the answer is solved like this :

2x-x+1=0

(x-1) X 2=0

x=1

Answer 5

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Answer 6

x2-x+1=0
(x-1)2=0
x=1

Answer 7

x^2-5x+1=0 x=((5+-sqrt(25-4))/2

x=(5+sqrt(21))/2 and x= ((5-sqrtr(21))/2