3z^2-36z+13=0

Simple and best practice solution for 3z^2-36z+13=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 3z^2-36z+13=0 equation:


Simplifying
3z2 + -36z + 13 = 0

Reorder the terms:
13 + -36z + 3z2 = 0

Solving
13 + -36z + 3z2 = 0

Solving for variable 'z'.

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

Divide each side by '3'.
4.333333333 + -12z + z2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + -12z + -4.333333333 + z2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + -12z + z2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + -12z + z2 = 0 + -4.333333333
-12z + z2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
-12z + z2 = -4.333333333

The z term is -12z.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12z + 36 + z2 = -4.333333333 + 36

Reorder the terms:
36 + -12z + z2 = -4.333333333 + 36

Combine like terms: -4.333333333 + 36 = 31.666666667
36 + -12z + z2 = 31.666666667

Factor a perfect square on the left side:
(z + -6)(z + -6) = 31.666666667

Calculate the square root of the right side: 5.627314339

Break this problem into two subproblems by setting 
(z + -6) equal to 5.627314339 and -5.627314339.

Subproblem 1

z + -6 = 5.627314339 Simplifying z + -6 = 5.627314339 Reorder the terms: -6 + z = 5.627314339 Solving -6 + z = 5.627314339 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = 5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + z = 5.627314339 + 6 z = 5.627314339 + 6 Combine like terms: 5.627314339 + 6 = 11.627314339 z = 11.627314339 Simplifying z = 11.627314339

Subproblem 2

z + -6 = -5.627314339 Simplifying z + -6 = -5.627314339 Reorder the terms: -6 + z = -5.627314339 Solving -6 + z = -5.627314339 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + z = -5.627314339 + 6 Combine like terms: -6 + 6 = 0 0 + z = -5.627314339 + 6 z = -5.627314339 + 6 Combine like terms: -5.627314339 + 6 = 0.372685661 z = 0.372685661 Simplifying z = 0.372685661

Solution

The solution to the problem is based on the solutions from the subproblems. z = {11.627314339, 0.372685661}

See similar equations:

| 1.5x+y=154 | | -6+8x=6x+10 | | 7*-3= | | x(8-x)+1x=-2 | | 5p^2+9pq+4q= | | 4x^2-17x+31=7x+4 | | x-9=-3/2x | | (-7)*(-3)= | | 3(4r-5)=2(7r-3) | | 9u-2u+2b= | | 5p^2-9pq+4q= | | 4n-3a=2n+2a | | 4y=5+6y-2 | | 2x^2-3x-20=0 | | 10x^3-105x^2+3=0 | | -12y+3x=96 | | 6(x+7)-8x=7x | | (T/p)m | | H=-81t^2+are+d | | 5x^2-42x-27=0 | | 4b^2+20b+25=20 | | 10(x+16)=-2(3-x) | | 5u-10=u+46+873875 | | X+25x+(x-37)=126 | | 6(x+7)-8=7 | | 3x+1=x+-3 | | 0.15x=0.08x+40 | | 3n+5+4n= | | .15x=.08x-40 | | 3x-6=12+x | | 1/5x-2/3(15)=30 | | 8x^2-10x+3=0 |

Equations solver categories