-3x^2-31x+23=0

Simple and best practice solution for -3x^2-31x+23=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^2-31x+23=0 equation: 


Simplifying
-3x2 + -31x + 23 = 0

Reorder the terms:
23 + -31x + -3x2 = 0

Solving
23 + -31x + -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'.
-7.666666667 + 10.33333333x + x2 = 0

Move the constant term to the right:

Add '7.666666667' to each side of the equation.
-7.666666667 + 10.33333333x + 7.666666667 + x2 = 0 + 7.666666667

Reorder the terms:
-7.666666667 + 7.666666667 + 10.33333333x + x2 = 0 + 7.666666667

Combine like terms: -7.666666667 + 7.666666667 = 0.000000000
0.000000000 + 10.33333333x + x2 = 0 + 7.666666667
10.33333333x + x2 = 0 + 7.666666667

Combine like terms: 0 + 7.666666667 = 7.666666667
10.33333333x + x2 = 7.666666667

The x term is 10.33333333x.  Take half its coefficient (5.166666665).
Square it (26.69444443) and add it to both sides.

Add '26.69444443' to each side of the equation.
10.33333333x + 26.69444443 + x2 = 7.666666667 + 26.69444443

Reorder the terms:
26.69444443 + 10.33333333x + x2 = 7.666666667 + 26.69444443

Combine like terms: 7.666666667 + 26.69444443 = 34.361111097
26.69444443 + 10.33333333x + x2 = 34.361111097

Factor a perfect square on the left side:
(x + 5.166666665)(x + 5.166666665) = 34.361111097

Calculate the square root of the right side: 5.86183513

Break this problem into two subproblems by setting 
(x + 5.166666665) equal to 5.86183513 and -5.86183513.


Subproblem 1
x + 5.166666665 = 5.86183513

Simplifying
x + 5.166666665 = 5.86183513

Reorder the terms:
5.166666665 + x = 5.86183513

Solving
5.166666665 + x = 5.86183513

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = 5.86183513 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = 5.86183513 + -5.166666665
x = 5.86183513 + -5.166666665

Combine like terms: 5.86183513 + -5.166666665 = 0.695168465
x = 0.695168465

Simplifying
x = 0.695168465


Subproblem 2
x + 5.166666665 = -5.86183513

Simplifying
x + 5.166666665 = -5.86183513

Reorder the terms:
5.166666665 + x = -5.86183513

Solving
5.166666665 + x = -5.86183513

Solving for variable 'x'.

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

Add '-5.166666665' to each side of the equation.
5.166666665 + -5.166666665 + x = -5.86183513 + -5.166666665

Combine like terms: 5.166666665 + -5.166666665 = 0.000000000
0.000000000 + x = -5.86183513 + -5.166666665
x = -5.86183513 + -5.166666665

Combine like terms: -5.86183513 + -5.166666665 = -11.028501795
x = -11.028501795

Simplifying
x = -11.028501795


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.695168465, -11.028501795}

See similar equations:

| 5x+10andy=-9x+17 | | 7s-10=-9+8s | | 10(-n-5)+7n=-9n+1 | | -2+4u=-30 | | a(5a-12)=0 | | 4a=39 | | 28-9(-20)=-12-11(-20) | | 2x+3x-5x+1x=equation | | 4f-17=-25 | | 0.25x=0.2x-25 | | 7.5=5.5x+25 | | 2x+3x-5x+1x= | | 6f+-6=8f+2 | | 6=2p-10 | | 3m+150=495 | | 3(2+b)+2b= | | R-9=7t-11 | | 2x+20+60=180 | | w^4-w^2-9= | | 2812.5=150x-2x^2 | | Y=2(x+10)+1 | | 7x+3=-15+x | | 0.444444444(z-18)-30=6 | | 49x=37 | | 4y-8=we | | 4(t-5)+(7t+1)= | | (x)+(x+1)+(x+2)=264 | | 4y-8x=2x | | 2x+20+46=180 | | -6x+17=29 | | 7(8a-4)= | | 3(y-3)+4y=7 |

Equations solver categories