3x^2-3x-31=0

Simple and best practice solution for 3x^2-3x-31=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 3x^2-3x-31=0 equation:


Simplifying
3x2 + -3x + -31 = 0

Reorder the terms:
-31 + -3x + 3x2 = 0

Solving
-31 + -3x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-10.33333333 + -1x + x2 = 0

Move the constant term to the right:

Add '10.33333333' to each side of the equation.
-10.33333333 + -1x + 10.33333333 + x2 = 0 + 10.33333333

Reorder the terms:
-10.33333333 + 10.33333333 + -1x + x2 = 0 + 10.33333333

Combine like terms: -10.33333333 + 10.33333333 = 0.00000000
0.00000000 + -1x + x2 = 0 + 10.33333333
-1x + x2 = 0 + 10.33333333

Combine like terms: 0 + 10.33333333 = 10.33333333
-1x + x2 = 10.33333333

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 = 10.33333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 10.33333333 + 0.25

Combine like terms: 10.33333333 + 0.25 = 10.58333333
0.25 + -1x + x2 = 10.58333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 10.58333333

Calculate the square root of the right side: 3.253203549

Break this problem into two subproblems by setting 
(x + -0.5) equal to 3.253203549 and -3.253203549.

Subproblem 1

x + -0.5 = 3.253203549 Simplifying x + -0.5 = 3.253203549 Reorder the terms: -0.5 + x = 3.253203549 Solving -0.5 + x = 3.253203549 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 = 3.253203549 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.253203549 + 0.5 x = 3.253203549 + 0.5 Combine like terms: 3.253203549 + 0.5 = 3.753203549 x = 3.753203549 Simplifying x = 3.753203549

Subproblem 2

x + -0.5 = -3.253203549 Simplifying x + -0.5 = -3.253203549 Reorder the terms: -0.5 + x = -3.253203549 Solving -0.5 + x = -3.253203549 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 = -3.253203549 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.253203549 + 0.5 x = -3.253203549 + 0.5 Combine like terms: -3.253203549 + 0.5 = -2.753203549 x = -2.753203549 Simplifying x = -2.753203549

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.753203549, -2.753203549}

See similar equations:

| 2x^2+12x+36=7 | | 5(a-3)=100 | | -x-0.2x=9 | | x+1/2x=27 | | (u-5)*9=54 | | (u-8)*9=54 | | (q-6)*6=54 | | 11+2.1=26 | | -10(s+5)=-86 | | -10(s*5)=-86 | | -y=7x+56 | | 2(f-1)=-8 | | -6(2t+2)=0 | | (x*x)+(2x)+(1)=4 | | 2(4w+10)=-27 | | -90=-9(6+2z) | | -5x-7x=24 | | x+5*5=70 | | 7x-16=(x+8)+4x | | 5(y+5)+4=49 | | 5(3s+4)=215 | | 5(2l+7)=95 | | [4x]+9=9 | | 5(a-6)=50 | | (u+3)*7=42 | | (q-10)*2=12 | | x-(3x+8)=12 | | (e+1)*4=16 | | 3x^4-10x+12=0 | | 6(4w+2)=16 | | -5(2t+7)=-85 | | -10(s+5)=-132 |

Equations solver categories