9z^2-36z+34=0

Simple and best practice solution for 9z^2-36z+34=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 9z^2-36z+34=0 equation:


Simplifying
9z2 + -36z + 34 = 0

Reorder the terms:
34 + -36z + 9z2 = 0

Solving
34 + -36z + 9z2 = 0

Solving for variable 'z'.

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

Divide each side by '9'.
3.777777778 + -4z + z2 = 0

Move the constant term to the right:

Add '-3.777777778' to each side of the equation.
3.777777778 + -4z + -3.777777778 + z2 = 0 + -3.777777778

Reorder the terms:
3.777777778 + -3.777777778 + -4z + z2 = 0 + -3.777777778

Combine like terms: 3.777777778 + -3.777777778 = 0.000000000
0.000000000 + -4z + z2 = 0 + -3.777777778
-4z + z2 = 0 + -3.777777778

Combine like terms: 0 + -3.777777778 = -3.777777778
-4z + z2 = -3.777777778

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -3.777777778 + 4

Reorder the terms:
4 + -4z + z2 = -3.777777778 + 4

Combine like terms: -3.777777778 + 4 = 0.222222222
4 + -4z + z2 = 0.222222222

Factor a perfect square on the left side:
(z + -2)(z + -2) = 0.222222222

Calculate the square root of the right side: 0.471404521

Break this problem into two subproblems by setting 
(z + -2) equal to 0.471404521 and -0.471404521.

Subproblem 1

z + -2 = 0.471404521 Simplifying z + -2 = 0.471404521 Reorder the terms: -2 + z = 0.471404521 Solving -2 + z = 0.471404521 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = 0.471404521 + 2 Combine like terms: -2 + 2 = 0 0 + z = 0.471404521 + 2 z = 0.471404521 + 2 Combine like terms: 0.471404521 + 2 = 2.471404521 z = 2.471404521 Simplifying z = 2.471404521

Subproblem 2

z + -2 = -0.471404521 Simplifying z + -2 = -0.471404521 Reorder the terms: -2 + z = -0.471404521 Solving -2 + z = -0.471404521 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + z = -0.471404521 + 2 Combine like terms: -2 + 2 = 0 0 + z = -0.471404521 + 2 z = -0.471404521 + 2 Combine like terms: -0.471404521 + 2 = 1.528595479 z = 1.528595479 Simplifying z = 1.528595479

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.471404521, 1.528595479}

See similar equations:

| 9[(z+4)-17]-[2(z-3)+2]= | | x+120+70+89= | | 3m+6=5m-58 | | 8x+4=11x-26 | | 8b-1=5b+8 | | (4x-1)+7x=10 | | y+1.55=9.23 | | 8n^2+10n-3=0 | | -4x+7+5x=5+x+2 | | 4(x)+5(x)=18 | | 5d+5= | | -2(3+x)=4 | | 48-11m=-7 | | x+(x+1)+(x+2)=81 | | 1.5b+8+2.5b-10=18 | | -5(x+4)-7=3 | | -4x^2y(-3xy^3)= | | 2y=12-6x | | -3x-9y=4 | | 12=-(6x-3) | | 2y=6z | | x+(x-2)=106 | | 3n-(18+5n)=4 | | 100[0.04(p+3)]= | | 3(3y+10)=120 | | 4n-12=n+4 | | 4.05+14.40=4.5(p+3) | | M+4=-5 | | 49=x-3.8 | | 10X+100=1100 | | x+1/14=2x-12 | | 8x-37=180 |

Equations solver categories