x^2-5x=2x+3

Simple and best practice solution for x^2-5x=2x+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 x^2-5x=2x+3 equation:


Simplifying
x2 + -5x = 2x + 3

Reorder the terms:
-5x + x2 = 2x + 3

Reorder the terms:
-5x + x2 = 3 + 2x

Solving
-5x + x2 = 3 + 2x

Solving for variable 'x'.

Reorder the terms:
-3 + -5x + -2x + x2 = 3 + 2x + -3 + -2x

Combine like terms: -5x + -2x = -7x
-3 + -7x + x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-3 + -7x + x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-3 + -7x + x2 = 0 + 2x + -2x
-3 + -7x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-3 + -7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -7x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -7x + x2 = 0 + 3

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

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

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 = 3 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + -7x + x2 = 15.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + -3.5 = 3.905124838 Simplifying x + -3.5 = 3.905124838 Reorder the terms: -3.5 + x = 3.905124838 Solving -3.5 + x = 3.905124838 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 = 3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.905124838 + 3.5 x = 3.905124838 + 3.5 Combine like terms: 3.905124838 + 3.5 = 7.405124838 x = 7.405124838 Simplifying x = 7.405124838

Subproblem 2

x + -3.5 = -3.905124838 Simplifying x + -3.5 = -3.905124838 Reorder the terms: -3.5 + x = -3.905124838 Solving -3.5 + x = -3.905124838 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 = -3.905124838 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.905124838 + 3.5 x = -3.905124838 + 3.5 Combine like terms: -3.905124838 + 3.5 = -0.405124838 x = -0.405124838 Simplifying x = -0.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.405124838, -0.405124838}

See similar equations:

| 4x^2-15x+17=-2x+8 | | 12h+9=-2h-11 | | x^2-14-4=0 | | 67-3x=6x+16 | | 6-10x=186-45x | | 2(4x+6)=4(2x+3) | | x^2+3x+2=-3x-3 | | n+2=(-14)-n | | (-17)-(-22)= | | 2x+9+x^2=3 | | (5x+20)=(3x+42) | | x^2+9x+10=2 | | x+3-3=6 | | (-8)-x=x-4x | | n^2-81=0 | | 12(2x+11)=12(2x+12) | | 2p+2m=16 | | 5(x+4)=9x+1 | | 4(2x-3)=3x+62 | | s^2-1=0 | | -4(2p+2)-23=5(5p+7) | | y^2-16=0 | | y^2-100=0 | | a^2=100 | | 5x+6=30y | | 12x-18x^2=0 | | X+10=2(x-9)-x | | 12+3y=4x | | 0.60x+0.40(100-x)=140 | | x(2x-7)=15 | | 2x+18=6y | | 2(x-3)=4(x-4) |

Equations solver categories