3x^2-69x+5=0

Simple and best practice solution for 3x^2-69x+5=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^2-69x+5=0 equation:


Simplifying
3x2 + -69x + 5 = 0

Reorder the terms:
5 + -69x + 3x2 = 0

Solving
5 + -69x + 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'.
1.666666667 + -23x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -23x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -23x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -23x + x2 = 0 + -1.666666667
-23x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-23x + x2 = -1.666666667

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -1.666666667 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -1.666666667 + 132.25

Combine like terms: -1.666666667 + 132.25 = 130.583333333
132.25 + -23x + x2 = 130.583333333

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 130.583333333

Calculate the square root of the right side: 11.427306478

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.427306478 and -11.427306478.

Subproblem 1

x + -11.5 = 11.427306478 Simplifying x + -11.5 = 11.427306478 Reorder the terms: -11.5 + x = 11.427306478 Solving -11.5 + x = 11.427306478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.427306478 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.427306478 + 11.5 x = 11.427306478 + 11.5 Combine like terms: 11.427306478 + 11.5 = 22.927306478 x = 22.927306478 Simplifying x = 22.927306478

Subproblem 2

x + -11.5 = -11.427306478 Simplifying x + -11.5 = -11.427306478 Reorder the terms: -11.5 + x = -11.427306478 Solving -11.5 + x = -11.427306478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.427306478 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.427306478 + 11.5 x = -11.427306478 + 11.5 Combine like terms: -11.427306478 + 11.5 = 0.072693522 x = 0.072693522 Simplifying x = 0.072693522

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.927306478, 0.072693522}

See similar equations:

| 2(3)+3y=12 | | 3x-2(x+4)=7 | | 2n=12n-30 | | 0.2(x-3)-x=0.2 | | 104r-4r^2=5 | | 4r^2-104r+5=0 | | w*-4=6 | | 5x+10=4x+21 | | 4x^2y^3-12x^3y^2= | | X-y-3=0 | | =(a+b+c)(a+b+c)(a+b+c) | | d+1=-3 | | =(a+b+c)(a+b+c) | | 4x-6x+x+10x-12= | | a-5=0 | | b+5=4 | | k-4=4 | | b*8=2 | | y=-3logx | | n*3=10 | | x+3x=2x-10 | | (a+b+c)= | | z-8=2 | | x^3-2x^2+3x=0 | | r-7=1 | | 2a(2a+7)-4+2=10 | | 36p^2-48p=0 | | x^5-2x^4+x^3=0 | | 3x^2-6px+4p=0 | | (4-5u)*(4+5u)= | | 25u^2= | | t^3-3t^2+4=0 |

Equations solver categories