3x^2-3x=5

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


Simplifying
3x2 + -3x = 5

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

Solving
-3x + 3x2 = 5

Solving for variable 'x'.

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

Combine like terms: 5 + -5 = 0
-5 + -3x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + -1x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + -1x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.666666667
-1x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
-1x + x2 = 1.666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.666666667 + 0.25

Combine like terms: 1.666666667 + 0.25 = 1.916666667
0.25 + -1x + x2 = 1.916666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.916666667

Calculate the square root of the right side: 1.384437311

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.384437311 and -1.384437311.

Subproblem 1

x + -0.5 = 1.384437311 Simplifying x + -0.5 = 1.384437311 Reorder the terms: -0.5 + x = 1.384437311 Solving -0.5 + x = 1.384437311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.384437311 + 0.5 x = 1.384437311 + 0.5 Combine like terms: 1.384437311 + 0.5 = 1.884437311 x = 1.884437311 Simplifying x = 1.884437311

Subproblem 2

x + -0.5 = -1.384437311 Simplifying x + -0.5 = -1.384437311 Reorder the terms: -0.5 + x = -1.384437311 Solving -0.5 + x = -1.384437311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.384437311 + 0.5 x = -1.384437311 + 0.5 Combine like terms: -1.384437311 + 0.5 = -0.884437311 x = -0.884437311 Simplifying x = -0.884437311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.884437311, -0.884437311}

See similar equations:

| 4(10a+11)-4=6(6a-6) | | n^2+16n-63= | | 6x=7.44 | | 3x^2-4x+36=0 | | (-2mn^6)(-13m^8n)= | | 8x-3-2x=45 | | 3x+7=12x-30 | | 35y^2-8y+3= | | 3x+9+4x=3 | | 20p=q | | q=20p | | 1x-24=8 | | 45+33=14 | | 4x^2+11x-3= | | (x+3)*5=2x+23 | | z^4-2z^2+1=0 | | 5x-2=x+4+2x | | 7y+14z=21 | | a^2+10ab+21b^2=0 | | 7a+14d=21 | | 4(x+3)-3=2(4-3x)-4 | | 7b+14c=21 | | 7a+14c=28 | | 7y+14b=21 | | 7a+14b=21 | | -(17-5s)-(9s+1)=58 | | 17+3w=8+21w | | 2x/5=4/7*65-x | | -5p=40 | | 3-2x+1=-6x-4 | | 7b+14y=28 | | 1+4y=6y-3 |

Equations solver categories