what is the value of x? please show your work.?

Question

(x-1)²/2 - (x-2)²/3 = (x-3)²/3

Answer 1

first multiply both sides by 6 to get:

3(x-1)^2 - 2(x-2)^2 = 2(x-3)^2

then distribute the exponents

3(x^2 - 2x + 1) - 2(x^2 - 4x + 4) = 2(x^2 - 6x + 9)

then distribute the numerical coefficients to the values within the parentheses:

3x^2 - 6x + 3 - 2x^2 + 8x - 8 = 2x^2 - 12x + 18

then group the numbers with the same degree of coefficient

(3x^2 - 2x^2 - 2x^2) - (6x - 8x - 12x) + (3 - 8 - 18) = 0

simplify

3x^2 - 14x - 23 = 0

this is quite difficult to factor, so just use the quadratic equation to solve for the value of x

Answer 2

First, multiply through by 6 to get 3(x - 1)^2 - 2(x - 2)^2 = 2(x - 3)^2. Now multiply out to get 3(x^2 - 2x + 1) - 2(x^2 - 4x + 4) = 2(x^2 - 6x + 9). Distribute to get 3x^2 - 6x + 3 - 2x^2 + 8x - 8 = 2x^2 - 12x + 18. Combine terms to get x^2 + 2x - 5 = 2x^2 - 12x + 18, and again to get x^2 - 14x + 23 = 0. From there, apply the quadratic formula because this cannot be factored.

Answer 3

First multiply each term by 2 and 3:

3(x-1)^2-2(x-2)^2=
2(x-3)^2

Expand the terms within the parenthesis:

3(x^2-2x+1)-2(x^2-4x+4)=
2(x^2-6x+9)

Remove all the parentheses:

3x^2-6x+3-2x^2+8x-8=
2x^2-12x+18

Transpose to the left side the terms on the right side:

3x^2-6x+3-2x^2+8x-8
-2x^2+12x-18=0

Simplify:

-x^2+14x-23=0

Multiply each term by -1:

x^2-14x+23=0

Use the formula
x=[-b+(b^2-4ac)^1/2]/2a, and
x=[-b-(b^2-4ac)^1/2]/2a

where a, b, and c, are the coefficients of the 1st,
2nd, and 3rd terms, respectively.

Note: Please check this formula. I haven't used it
for ages.

If it is correct, substitute the values of a,b,c in the formula:

x={14+[-14^2-4(1)(23)]^1/2}/2
=[14+(196-92)^1/2]/2
=[14+(104)^1/2]/2
=(14+10.2)/2
=(24.2)/2
=12.1

The other value of x would be:

x=(14-10.2)/2
=3.8/2
=1.9

Answer 4

Multiply by 6


3 (x-1)² - 2(x-2)² = 2(x-3)²
3 (x^2 -2x+1) -2(x^2-4x+4) = 2(X^2 -6X+9)
3x^2 -6X +3 -2x^2 +8X -8 = 2X^2 -12X +18
X^2 +2x -5 = - 12X +18
x^2 +14X -23 = 0

a=1, b=14, c= -23

Answer 5

(x-1)²/2 - (x-2)²/3 = (x-3)²/3

(x^2 - 2X + 1)/ 2 - (x^2 -4x + 4)/3 = (x^2 -6x +9)/3

multiply by 3 all over
3/2 (x^2 - 2x + 1) - x^2 + 4x -4 = x^2 - 6x + 9
=>
3/2 (x^2 - 2x + 1) = 2x^2 -10x +13

3x^2 - 6x + 3 = 4x^2 - 20x + 26
=>

0 = x^2 - 14x + 23

Answer 6

3(x-1)^2-2(x-2)^2=2(x-3)^2
3x^2-6x+3-2x^2+8x-8=2x^2-12x+18
-x^2+14x-23=0
x^2-14x+23=0
use the quadratic formula to solve

Answer 7

x is a number to be found by a student to reinforce what he has learned in school.

please show your work..... neatness is a big plus

Answer 8

{[x-1]^2}/2-{[x-2]^2}/3={[x-3]^2}/3
[x^2-2x+1]3-[x^2-4x+4]2-[x^2-6x+9]2=0
3x^2-6x+3
-2x^2+8x-8
-2x^2+12x-18=0
-x^2+14x-23=0
x^2-14x+23=0
x={14+-sqrt[196-92]}/2
=7+-sqrt26