3x^2-6x-7=x^2+3x-x(x-1)+3

Simple and best practice solution for 3x^2-6x-7=x^2+3x-x(x-1)+3 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 3x^2-6x-7=x^2+3x-x(x-1)+3 equation: 


Simplifying
3x2 + -6x + -7 = x2 + 3x + -1x(x + -1) + 3

Reorder the terms:
-7 + -6x + 3x2 = x2 + 3x + -1x(x + -1) + 3

Reorder the terms:
-7 + -6x + 3x2 = x2 + 3x + -1x(-1 + x) + 3
-7 + -6x + 3x2 = x2 + 3x + (-1 * -1x + x * -1x) + 3
-7 + -6x + 3x2 = x2 + 3x + (1x + -1x2) + 3

Reorder the terms:
-7 + -6x + 3x2 = 3 + 3x + 1x + x2 + -1x2

Combine like terms: 3x + 1x = 4x
-7 + -6x + 3x2 = 3 + 4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-7 + -6x + 3x2 = 3 + 4x + 0
-7 + -6x + 3x2 = 3 + 4x

Solving
-7 + -6x + 3x2 = 3 + 4x

Solving for variable 'x'.

Reorder the terms:
-7 + -3 + -6x + -4x + 3x2 = 3 + 4x + -3 + -4x

Combine like terms: -7 + -3 = -10
-10 + -6x + -4x + 3x2 = 3 + 4x + -3 + -4x

Combine like terms: -6x + -4x = -10x
-10 + -10x + 3x2 = 3 + 4x + -3 + -4x

Reorder the terms:
-10 + -10x + 3x2 = 3 + -3 + 4x + -4x

Combine like terms: 3 + -3 = 0
-10 + -10x + 3x2 = 0 + 4x + -4x
-10 + -10x + 3x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-10 + -10x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-3.333333333 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -3.333333333x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -3.333333333x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + 3.333333333
-3.333333333x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-3.333333333x + x2 = 3.333333333

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 3.333333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 3.333333333 + 2.777777779

Combine like terms: 3.333333333 + 2.777777779 = 6.111111112
2.777777779 + -3.333333333x + x2 = 6.111111112

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 6.111111112

Calculate the square root of the right side: 2.472066163

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.472066163 and -2.472066163.


Subproblem 1
x + -1.666666667 = 2.472066163

Simplifying
x + -1.666666667 = 2.472066163

Reorder the terms:
-1.666666667 + x = 2.472066163

Solving
-1.666666667 + x = 2.472066163

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.472066163 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.472066163 + 1.666666667
x = 2.472066163 + 1.666666667

Combine like terms: 2.472066163 + 1.666666667 = 4.13873283
x = 4.13873283

Simplifying
x = 4.13873283


Subproblem 2
x + -1.666666667 = -2.472066163

Simplifying
x + -1.666666667 = -2.472066163

Reorder the terms:
-1.666666667 + x = -2.472066163

Solving
-1.666666667 + x = -2.472066163

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.472066163 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.472066163 + 1.666666667
x = -2.472066163 + 1.666666667

Combine like terms: -2.472066163 + 1.666666667 = -0.805399496
x = -0.805399496

Simplifying
x = -0.805399496


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.13873283, -0.805399496}

See similar equations:

| -4(3y-10)+3(2y+6)= | | 12y-(9y)=144 | | 0=n/2-4 | | -8y+48=2(y+9) | | 2u-6=-18 | | .75(3t+14)-.75(3t-2)=12 | | 2x=29x-7(6+5) | | .6(x-1)=.08 | | m(m-6)(2m+3)=0 | | 2a^2+22a+60=0 | | b=8cmh | | s=7.15+.35s | | 0.2b+3=0.5b+12 | | s=7.15+.35x | | 3x-22=14 | | 6y^2-13y+5=0 | | .7(4x+.3)=41.65 | | 2y^2+3y-5=0 | | [3-(5+3*2)]-3= | | -2(v-7)=-7+44 | | .58n-.86=4.592 | | 6g+4(-3+3g)=1-g | | 2x^2+10x=-16 | | 6(4x-2)=12 | | 1/12(48+24b)=2(17-4b) | | 6g+4(-3+g)=1-g | | -4x+9x=30 | | 125-85= | | 7-7x=21+3x | | (6x-15)=(2x+5) | | 7-n=21+3-n | | 2x^2+16x-66=0 |

Equations solver categories