x^2-3x=7x-2 solve using qradratic formula?

we have x^2 -3x= 7x -2 equal to x^2- 3x -7x +2 =0
so we have x^2 -10x +2 =0 equal to ( x^2 -10x +25) -25 +2=0
So we have (x -5 )^2 = 23 <=> x+5=+ √23 or x+5= - √23
so we have 2 answer :x=5 + √23 ANDx= 5 - √23

Question Number 1 :
For this equation x^2 - 3*x = 7*x - 2 , answer the following questions :
A. Find the roots using Quadratic Formula !

Answer Number 1 :
First, we have to turn equation : x^2 - 3*x = 7*x - 2 , into a*x^2+b*x+c=0 form.
x^2 - 3*x = 7*x - 2 , move everything in the right hand side, to the left hand side of the equation
<=> x^2 - 3*x - ( 7*x - 2 ) = 0 , which is the same with
<=> x^2 - 3*x + ( - 7*x + 2 ) =0 , now open the bracket and we get
<=> x^2 - 10*x + 2 = 0

The equation x^2 - 10*x + 2 = 0 is already in a*x^2+b*x+c=0 form.
In that form, we can easily derive that the value of a = 1, b = -10, c = 2.

1A. Find the roots using Quadratic Formula !
Use abc formula and you get either
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) or x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
We had know that a = 1, b = -10 and c = 2,
we just need to subtitute the value of a,b and c in the abc formula.
So x1 = (-(-10) + sqrt( (-10)^2 - 4 * (1)*(2)))/(2*1) and x2 = (-(-10) - sqrt( (-10)^2 - 4 * (1)*(2)))/(2*1)
Which is the same with x1 = ( 10 + sqrt( 100-8))/(2) and x2 = ( 10 - sqrt( 100-8))/(2)
Which make x1 = ( 10 + sqrt( 92))/(2) and x2 = ( 10 - sqrt( 92))/(2)
Which make x1 = 5 + sqrt( 23) and x2 = 5 - sqrt(23)


The answers are x1 = 9.79583152331272 and x2 = 0.204168476687281

x² - 10x + 2 = 0
x = [ 10 ± √ (100 - 8 ) ] / 2
x = [ 10 ± √ (92) ] / 2
x = [ 10 ± 2√23 ] / 2
x = 5 ± √23

x^2 - 3x = 7x - 2
x^2 - 3x - 7x + 2 = 0
x^2 - 10x + 2 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -10
c = 2

x = [10 ±√(100 - 8)]/2
x = [10 ±√92]/2
x = [10 ±9.59]/2 (approx.)

x = [10 + 9.59]/2
x = 19.59/2
x = 9.795

x = [10 - 9.59]/2
x = 0.41/2
x = 0.205

∴ x = 9.795 , 0.205 (approx.)

x² - 3x = 7x - 2

First, rearrange the equation so you get it equal to 0:

x² - 3x - 7x + 2 = 0
x² - 10x + 2 = 0

Now you can proceed to use the formula in the form (ax² + bx + c = 0)

x = [-b ± √(b² - 4ac)] / 2a

x = [10 ± √((-10)² - 4*1*2)] / 2(1)

x = [10 ± √(100 - 8)] / 2

x = (10 ± √92) / 2

x = (10 ± 2√23) / 2

x = 5 + √23 AND 5 - √23