Solve the quadratic formula: x^2-2x=15x-10 (show work)?

x^2 - 2x = 15x - 10
x^2 - 2x - 15x + 10 = 0
x^2 - 17x + 10 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 1
b = -17
c = 10

x = [17 ±√(289 - 40)]/2
x = [17 ±√249]/2

∴ x = [17 ±√249]/2

Hi,

x² - 2x = 15x - 10

x² - 17x + 10 = 0
. . . . . . .____________
-(-17) ± √(-17)² - 4(1)(10)
----------------------------------- = x
. . . . . .2(1)

. . . . ._______
17 ± √289 - 40
---------------------- = x
. . . . . .2

. . . . .___
17 ± √249
---------------- = x <==ANSWER
. . . .2

I hope that helps!! :-)

Question Number 1 :
For this equation x^2 - 2*x = 15*x - 10 , answer the following questions :
A. Find the roots using Quadratic Formula !
B. Use completing the square to find the root of the equation !

Answer Number 1 :
First, we have to turn equation : x^2 - 2*x = 15*x - 10 , into a*x^2+b*x+c=0 form.
x^2 - 2*x = 15*x - 10 , move everything in the right hand side, to the left hand side of the equation
<=> x^2 - 2*x - ( 15*x - 10 ) = 0 , which is the same with
<=> x^2 - 2*x + ( - 15*x + 10 ) =0 , now open the bracket and we get
<=> x^2 - 17*x + 10 = 0

The equation x^2 - 17*x + 10 = 0 is already in a*x^2+b*x+c=0 form.
By matching the constant position, we can derive that the value of a = 1, b = -17, c = 10.

1A. Find the roots using Quadratic Formula !
By using abc formula the value of x is both
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
As we know that a = 1, b = -17 and c = 10,
then the value a,b and c in the abc formula, can be subtituted.
So we get x1 = (-(-17) + sqrt( (-17)^2 - 4 * (1)*(10)))/(2*1) and x2 = (-(-17) - sqrt( (-17)^2 - 4 * (1)*(10)))/(2*1)
Which is the same as x1 = ( 17 + sqrt( 289-40))/(2) and x2 = ( 17 - sqrt( 289-40))/(2)
Which is the same with x1 = ( 17 + sqrt( 249))/(2) and x2 = ( 17 - sqrt( 249))/(2)
We got x1 = ( 17 + 15.7797338380595 )/(2) and x2 = ( 17 - 15.7797338380595 )/(2)
So we got the answers as x1 = 16.3898669190297 and x2 = 0.61013308097025

1B. Use completing the square to find the root of the equation !
x^2 - 17*x + 10 = 0 ,divide both side with 1
So we get x^2 - 17*x + 10 = 0 ,
We know that the coefficient of x is -17
We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -17/2 = -8.5
By using that fact we turn the equation into x^2 - 17*x + 72.25 - 62.25 = 0
So we will get ( x - 8.5 )^2 - 62.25 = 0
And it is the same with (( x - 8.5 ) - 7.88986691902975 ) * (( x - 8.5 ) + 7.88986691902975 ) = 0
By opening the brackets we will get ( x - 8.5 - 7.88986691902975 ) * ( x - 8.5 + 7.88986691902975 ) = 0
Do the addition/subtraction, and we get ( x - 16.3898669190297 ) * ( x - 0.61013308097025 ) = 0
So we have the answers x1 = 16.3898669190297 and x2 = 0.61013308097025

x² - 17x + 10 = 0
x = [ 17 ± √ (289 - 40 ) ] / 2
x = [ 17 ± √ (249) ] / 2

use the quadratic formulae

first changes the formula into the general form
x^2 - 2x - 15x + 10 = 0
x^2 - 17x + 10 = 0
a = 1, b = -17 , c = 10

then the quadratic formula
x = ( -b + - ( b^2 - 4ac )^1/2 ) / 2a
Just substitute the numbers inside and the answer will be found

x^2-2x=15x-10
x^2 - 17x + 10 = 0

a = 1, b = -17, c = 10

x = (17 +/- root.( 17^2 - 4(1)(10)) ) / 2(1)

x = 16.4, 0.610

x^2-2x=15x-10
x^2-2x-15x=10
x^2-17x=10
i dont know how to show the formula

x^2-2x=15x-10
x^2-17x+10=0
x=(17+-sqrt(17^2-4×10))/2
x=(17+-sqrt(289-40))/2
x=(17+-sqrt(249))/2

That is it. I hope that you understand and good luck!

Move all the terms to the left side and set it equal to zero:

x^2 - 17x + 10 = 0

Then try to factor it [ it must be in the form ( x - ? ) ( x - ?) ] or use the quadratic formula, whichever works.