3x^2-69x+16=0

Simple and best practice solution for 3x^2-69x+16=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+16=0 equation:


Simplifying
3x2 + -69x + 16 = 0

Reorder the terms:
16 + -69x + 3x2 = 0

Solving
16 + -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'.
5.333333333 + -23x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -23x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -23x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -23x + x2 = 0 + -5.333333333
-23x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-23x + x2 = -5.333333333

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 = -5.333333333 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -5.333333333 + 132.25

Combine like terms: -5.333333333 + 132.25 = 126.916666667
132.25 + -23x + x2 = 126.916666667

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 126.916666667

Calculate the square root of the right side: 11.265729744

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.265729744 and -11.265729744.

Subproblem 1

x + -11.5 = 11.265729744 Simplifying x + -11.5 = 11.265729744 Reorder the terms: -11.5 + x = 11.265729744 Solving -11.5 + x = 11.265729744 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 = 11.265729744 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.265729744 + 11.5 x = 11.265729744 + 11.5 Combine like terms: 11.265729744 + 11.5 = 22.765729744 x = 22.765729744 Simplifying x = 22.765729744

Subproblem 2

x + -11.5 = -11.265729744 Simplifying x + -11.5 = -11.265729744 Reorder the terms: -11.5 + x = -11.265729744 Solving -11.5 + x = -11.265729744 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 = -11.265729744 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.265729744 + 11.5 x = -11.265729744 + 11.5 Combine like terms: -11.265729744 + 11.5 = 0.234270256 x = 0.234270256 Simplifying x = 0.234270256

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.765729744, 0.234270256}

See similar equations:

| 4(b-8)=3(2b+4) | | 2x-3/5÷5x-1=3/5 | | 0=5y+20 | | .19x+.11y=1.16 | | (2x+5x)*1=5000 | | 4sqrt(25x^2)= | | -5(x-3)=5*(x-1) | | y=40x-3 | | z^5y/z^3y^4 | | sqrt(25x)+4sqrtx= | | (x)=x^2-6x+5 | | 8x+78+2x+144=180 | | 5(x-3)=-2x-4 | | 8u+8=3u+29 | | 12+0(5-7)=x | | 8x-3+5x+21=180 | | 2x+7+3x=12 | | -1x-24=3x-2 | | 4y+20=16y+17 | | 12x+32=21+x | | 1/3=t/9 | | 5m-9=4m | | 4x+3y-(-2x+5y)= | | 5x-20=4y | | 4x+3y-(-2+5y)= | | 4(u-2)-7u=16 | | mk=0.5(n-k) | | Y=65*4 | | 1/2x=1/4=x | | -4.8-5y-7.3-2y=6y+1.4 | | -4.8-5y-7.3-2y=6y | | 32v^4/4v^7 |

Equations solver categories