HELP if you are good at algebra!?

Question

Solve by completing the square :

x^2 - 3x = 2x - 1

If anyone can post a response with how they did it, I would really appreciate it!

Answer 1

x² - 3x = 2x - 1

x² - 3x - 2x = 2x - 1 - 2x

x² - 5x = - 1

x² - 5x + ____ = - 1 +_____

x² - 5x + 25/4 = - 1 + 25/4

(x - 5/2)(x - 5/2) = -4/4 + 25/4

(x - 5/2)² = 21/4

(√x - 5/2)² = ± √21/ √4

x - 5/2 = ± √21 / 2

x - 5/2 + 5/2 = 5/2 ± √21 / 2

x = 5/2 ± √21 / 2

- - - - - - - - - -s-

Answer 2

Ok, in algebra, what you should remember is what you do to one side (add, subtract, multiply, or divide), you must also do that to the other side.

To complete the squares, one should remember that:
(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2
You should also note that, if c ^ 2 = d ^ 2 then c = (+/-)d

First, try to isolate x to one side, I'd choose LHS:
x ^ 2 - 3x = 2x - 1
<=> x ^ 2 - 3x - 2x = 2x - 2x - 1 (subtract 2x from both sides)
<=> x ^ 2 - 5x = -1
<=> x ^ 2 - 2 * (5 / 2) x = -1 (Now, look at the form (a + b) ^ 2 above, you should add (5 / 2) ^ 2 to both sides, right?)
<=> x ^ 2 - 2 * (5 / 2) x + (5 / 2) ^ 2 = -1 + (5 / 2) ^ 2
<=> (x - 5/2) ^ 2 = -1 + 25 / 4
<=> (x - 5/2) ^ 2 = 21 / 4
<=> x - 5 / 2 = (+/-) sqrt(21) / 2
Can you complete the problem on your own? One last step. :)

Answer 3

x^2 - 3x = 2x - 1
Subtract 2x from both sides
x^2 - 5x = -1

To complete the square for x^2 + bx you add the square of HALF the coefficient of x [in this case you add (-5/2)^2] use the formula:
x^2 +bx + (b/2)^2 = (x + b/2)^2

x^2 - 5x + (-5/2)^2 = (-5/2)^2 - 1
Simplify
x^2 - 5x + (25/4) = (25/4) - (4/4) = 21/4
in order for two products to produce this -,+ the sign between them needs to be negative.. ex: (x - 1)^2 = x^2 -2x + 1
So you need (x - 5/2)^2
And you get
(x - 5/2)^2 = 21/4
Take the square-root of both sides (remember that you need both
the positive and the negative roots)
x - 5/2 = +/- sqrt(21/4)
So you have two solutions:
First the positive case:
x - 5/2 = sqrt(21/4) = sqrt[21 * (1/4)]
Extract the sqrt(1/4) = 1/2
(multiply by 1/2 is same as divide by 2 whichever way you prefer)
x - 5/2 = [sqrt(21)]/2
add 5/2 to both sides
x = [sqrt(21)]/2 + 5/2 = [sqrt(21) + 5]/2
Now the negative case
x - 5/2 = - sqrt(21/4)
Add 5/2 to both sides AND Extract sqrt(1/4)
x = - sqrt(21)/2 + 5/2
Rearrange a bit
x = 5/2 - sqrt(21)/2
Combine
x = [ 5 - sqrt(21)]/2

Now you should TEST the answers!!!! If they do NOT work, then you do not have a solution in real numbers.

Answer 4

Below are appropriate steps for solving your equation using completing the square method
x^2 - 3x - 2x + 1 = 0
x^2 - 5x = -1
x^2 - 5x + (5/2)^2 = -1 + (5/2)^2
x^2 - 5x + 25/4 = 21/4
(x-5/2)^2 = 21/4
(x-5/2) = +/- square root of (21/4)
x = (5/2) +/- [square root of (21/4)]

Answer 5

First bring the equation in the standard form ax^2 + bx + c = 0

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

Since straightforward factorization is not possible, use the formula

x = (-b +/- sqrt(b^2 - 4ac))/2a

x = (5 +/- sqrt(21))/2*1

therefore there are two real values of x

x= (5 + sqrt(21))/2
or
x= (5 - sqrt(21))/2

Answer 6

You have this now: x^2-5x+1=0 this is an equation like ax^2+bx+c=0. Then you define the D factor. The D factor is equal to D=b^2-4ac. If the D factor is higher than zero, you have 2 solutions for x. If it is Equal to zero you have one solution. If it is lower than zero the equation does not have a solution. Then the solution is X1= -b+(the square root of D)/2a, and X2=-b-(the square root of D)/2a. But please check it out with someone else. I am not sure I 've got it right.

Answer 7

x^2 - 3x = 2x - 1
first you want everything but the number on the left so
x^2-5x=-1
Then take the number in front of x and divide by 2
(x-5/2)^2=-1+(25/4) (25/4 is 5/2 squared)
(x-5/2)^2=5.25
x-5/2 = +-sqrt(5.25)
x=+-sqrt(5.25)+5/2

Answer 8

x²-3x=2x-1
<=> x²-5x+1=0
d=b²-4ac=25-4=21
x=1/2(5+sqrt(21)) or x=1/2(5-sqrt(21))

Answer 9

x^2-5x=-1

x^2-2*(5/2)*x+25/4=25/4-1=21/4

(x-5/2)^2=21/4

x-5/2=(+/-)square root of(21/4)

solvable from here.Hope this helps

Answer 10

x²-3x = 2x-1

x²-3x-2x+1=0

x²-5x+1=0

x=√5x+1

by using quadratic equation formula, we can get the value of x.

ax²+bx+c = 0

x= (b + √b²-4ac)/(2a)

x=[5+√(5)² -4(1)(1)]/[2(1)]

=(5+√25-4)/2

=(5+√21)/2

x = 4.79.................ans.

To check:

x²-3x=2x-1

(4.79)²-3(4.79) = 2(4.79)-1...... substitute the value of x.

22.9441-14.37 = 9.58-1

8.5 = 8.5