(2x-3)(x-3)-(x-1)(x-1)=0

Simple and best practice solution for (2x-3)(x-3)-(x-1)(x-1)=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for (2x-3)(x-3)-(x-1)(x-1)=0 equation:


Simplifying
(2x + -3)(x + -3) + -1(x + -1)(x + -1) = 0

Reorder the terms:
(-3 + 2x)(x + -3) + -1(x + -1)(x + -1) = 0

Reorder the terms:
(-3 + 2x)(-3 + x) + -1(x + -1)(x + -1) = 0

Multiply (-3 + 2x) * (-3 + x)
(-3(-3 + x) + 2x * (-3 + x)) + -1(x + -1)(x + -1) = 0
((-3 * -3 + x * -3) + 2x * (-3 + x)) + -1(x + -1)(x + -1) = 0
((9 + -3x) + 2x * (-3 + x)) + -1(x + -1)(x + -1) = 0
(9 + -3x + (-3 * 2x + x * 2x)) + -1(x + -1)(x + -1) = 0
(9 + -3x + (-6x + 2x2)) + -1(x + -1)(x + -1) = 0

Combine like terms: -3x + -6x = -9x
(9 + -9x + 2x2) + -1(x + -1)(x + -1) = 0

Reorder the terms:
9 + -9x + 2x2 + -1(-1 + x)(x + -1) = 0

Reorder the terms:
9 + -9x + 2x2 + -1(-1 + x)(-1 + x) = 0

Multiply (-1 + x) * (-1 + x)
9 + -9x + 2x2 + -1(-1(-1 + x) + x(-1 + x)) = 0
9 + -9x + 2x2 + -1((-1 * -1 + x * -1) + x(-1 + x)) = 0
9 + -9x + 2x2 + -1((1 + -1x) + x(-1 + x)) = 0
9 + -9x + 2x2 + -1(1 + -1x + (-1 * x + x * x)) = 0
9 + -9x + 2x2 + -1(1 + -1x + (-1x + x2)) = 0

Combine like terms: -1x + -1x = -2x
9 + -9x + 2x2 + -1(1 + -2x + x2) = 0
9 + -9x + 2x2 + (1 * -1 + -2x * -1 + x2 * -1) = 0
9 + -9x + 2x2 + (-1 + 2x + -1x2) = 0

Reorder the terms:
9 + -1 + -9x + 2x + 2x2 + -1x2 = 0

Combine like terms: 9 + -1 = 8
8 + -9x + 2x + 2x2 + -1x2 = 0

Combine like terms: -9x + 2x = -7x
8 + -7x + 2x2 + -1x2 = 0

Combine like terms: 2x2 + -1x2 = 1x2
8 + -7x + 1x2 = 0

Solving
8 + -7x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -7x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -7x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7x + x2 = 0 + -8
-7x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-7x + x2 = -8

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -8 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -8 + 12.25

Combine like terms: -8 + 12.25 = 4.25
12.25 + -7x + x2 = 4.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + -3.5 = 2.061552813 Simplifying x + -3.5 = 2.061552813 Reorder the terms: -3.5 + x = 2.061552813 Solving -3.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.061552813 + 3.5 x = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 x = 5.561552813 Simplifying x = 5.561552813

Subproblem 2

x + -3.5 = -2.061552813 Simplifying x + -3.5 = -2.061552813 Reorder the terms: -3.5 + x = -2.061552813 Solving -3.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.061552813 + 3.5 x = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 x = 1.438447187 Simplifying x = 1.438447187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.561552813, 1.438447187}

See similar equations:

| 3(3x-2)=(x+4)(4-x) | | F^2=x-B^2 | | -16t^2+36t-8=0 | | t(t+5)=2t^2+9 | | -5(2r-2)-7=-3(2r-5) | | X^4+12X^2-8=0 | | 8-9x=26 | | -6+2x=4 | | 3n-6=12 | | m=7/4(6-7) | | 3y-6=9 | | 3x-9=2x-2 | | 3x^3-14x^2-5x=0 | | 8n-24=40 | | 5z-1=z+19 | | 11-a=77 | | 5u+16=1 | | 4n+15n=47 | | 12x+15=32 | | 2+14x+3=1+5x+12+7x | | a+2b+3c=19 | | x^2-11x=28 | | -8=-2x | | 17x-2x+5=19+13x | | 4x-3=-2(x+4) | | 42+74= | | 7x+4+2x=16+3x | | (4x-5)=(5x-4) | | 13x+2=12x+9 | | -7x=-3x-24 | | (12x-15)=(20x-16) | | 5+4x+1=10+3 |

Equations solver categories