9z^2+76=54z

Simple and best practice solution for 9z^2+76=54z 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+76=54z equation:


Simplifying
9z2 + 76 = 54z

Reorder the terms:
76 + 9z2 = 54z

Solving
76 + 9z2 = 54z

Solving for variable 'z'.

Reorder the terms:
76 + -54z + 9z2 = 54z + -54z

Combine like terms: 54z + -54z = 0
76 + -54z + 9z2 = 0

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

Divide each side by '9'.
8.444444444 + -6z + z2 = 0

Move the constant term to the right:

Add '-8.444444444' to each side of the equation.
8.444444444 + -6z + -8.444444444 + z2 = 0 + -8.444444444

Reorder the terms:
8.444444444 + -8.444444444 + -6z + z2 = 0 + -8.444444444

Combine like terms: 8.444444444 + -8.444444444 = 0.000000000
0.000000000 + -6z + z2 = 0 + -8.444444444
-6z + z2 = 0 + -8.444444444

Combine like terms: 0 + -8.444444444 = -8.444444444
-6z + z2 = -8.444444444

The z term is -6z.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6z + 9 + z2 = -8.444444444 + 9

Reorder the terms:
9 + -6z + z2 = -8.444444444 + 9

Combine like terms: -8.444444444 + 9 = 0.555555556
9 + -6z + z2 = 0.555555556

Factor a perfect square on the left side:
(z + -3)(z + -3) = 0.555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(z + -3) equal to 0.745355993 and -0.745355993.

Subproblem 1

z + -3 = 0.745355993 Simplifying z + -3 = 0.745355993 Reorder the terms: -3 + z = 0.745355993 Solving -3 + z = 0.745355993 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = 0.745355993 + 3 Combine like terms: -3 + 3 = 0 0 + z = 0.745355993 + 3 z = 0.745355993 + 3 Combine like terms: 0.745355993 + 3 = 3.745355993 z = 3.745355993 Simplifying z = 3.745355993

Subproblem 2

z + -3 = -0.745355993 Simplifying z + -3 = -0.745355993 Reorder the terms: -3 + z = -0.745355993 Solving -3 + z = -0.745355993 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + z = -0.745355993 + 3 Combine like terms: -3 + 3 = 0 0 + z = -0.745355993 + 3 z = -0.745355993 + 3 Combine like terms: -0.745355993 + 3 = 2.254644007 z = 2.254644007 Simplifying z = 2.254644007

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.745355993, 2.254644007}

See similar equations:

| -12x+144=-9+(-16x) | | 8x^2+72x-16=0 | | -5s+8=2 | | b-26=108 | | Y=-3x^2+7x-3 | | w^2=8w-25 | | 3(x+6)=126 | | x=y^2-6y | | 108=2x^2-6x | | p/23=-27 | | H/59 | | (x-1)(x-2)(x-3)=60 | | 4x+3=135 | | 130+(4x-7)+(8x-39)=180 | | 252=(2x+12)(2x+16) | | 775=r-96 | | 81x^3+36x^4=0 | | -2/5=-10/t | | -2(4-3x)-6=10 | | 3x-2(x+4)=35 | | 3p-4=4p | | 2-1x+2x+1=0 | | 2x-16=-2x+2(2x-8) | | 15=s/18 | | -2x^2+144=0 | | 8x^2+8y^2+3x-6y=13 | | (X+7)(x+7)=22 | | 3x^2+190x-300=0 | | 2(x-1)=140 | | 4×q=16/2 | | 10x+10y=890 | | 12x-12=15x |

Equations solver categories