2x(2x-3)=6+x

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


Simplifying
2x(2x + -3) = 6 + x

Reorder the terms:
2x(-3 + 2x) = 6 + x
(-3 * 2x + 2x * 2x) = 6 + x
(-6x + 4x2) = 6 + x

Solving
-6x + 4x2 = 6 + x

Solving for variable 'x'.

Reorder the terms:
-6 + -6x + -1x + 4x2 = 6 + x + -6 + -1x

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

Reorder the terms:
-6 + -7x + 4x2 = 6 + -6 + x + -1x

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

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

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

Divide each side by '4'.
-1.5 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -1.75x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -1.75x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -1.75x + x2 = 0 + 1.5
-1.75x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-1.75x + x2 = 1.5

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 1.5 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1.5 + 0.765625

Combine like terms: 1.5 + 0.765625 = 2.265625
0.765625 + -1.75x + x2 = 2.265625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.505199322 and -1.505199322.

Subproblem 1

x + -0.875 = 1.505199322 Simplifying x + -0.875 = 1.505199322 Reorder the terms: -0.875 + x = 1.505199322 Solving -0.875 + x = 1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.505199322 + 0.875 x = 1.505199322 + 0.875 Combine like terms: 1.505199322 + 0.875 = 2.380199322 x = 2.380199322 Simplifying x = 2.380199322

Subproblem 2

x + -0.875 = -1.505199322 Simplifying x + -0.875 = -1.505199322 Reorder the terms: -0.875 + x = -1.505199322 Solving -0.875 + x = -1.505199322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -1.505199322 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.505199322 + 0.875 x = -1.505199322 + 0.875 Combine like terms: -1.505199322 + 0.875 = -0.630199322 x = -0.630199322 Simplifying x = -0.630199322

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.380199322, -0.630199322}

See similar equations:

| 5(4x-9)-7=5(x-3)+38 | | y^2+12y=-x^2-4x+16 | | 2p+-14p+16p=-4 | | 4.47=log(X) | | 4z-3z=17 | | 16=5h-9 | | 8/10×=24 | | 2w+8w=10 | | -2(k+2)-(-3k-9)=-7 | | D=v*t | | 27x-10y=15 | | -2x-3.6+0.4=-9 | | 9-2a=9+5 | | 8t+8=7t | | 3x^3=0.75x | | 2*-1-y=-9 | | 14.3=-1.4+3D | | 2*1-y=-9 | | 0=78+8x | | x+8.1=14.5 | | 5n^2+n+6=5 | | 5p-(1)(1-p)=2p+5(1-p) | | 160-15x=100 | | -2u+7x=13 | | 5p-(2)(1-p)=1p+5(1-p) | | 29(x+4)=5(6x-2) | | 17=8-3G | | 20=b/4 | | (2x+3)(x-1)=6x | | 0.0915t^2-0.938t+1.705=0 | | 2.5x^2+10x+15=0 | | 2(4x-9)=7x |

Equations solver categories