22z+22=7z^2+33z-48

Simple and best practice solution for 22z+22=7z^2+33z-48 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 22z+22=7z^2+33z-48 equation:


Simplifying
22z + 22 = 7z2 + 33z + -48

Reorder the terms:
22 + 22z = 7z2 + 33z + -48

Reorder the terms:
22 + 22z = -48 + 33z + 7z2

Solving
22 + 22z = -48 + 33z + 7z2

Solving for variable 'z'.

Reorder the terms:
22 + 48 + 22z + -33z + -7z2 = -48 + 33z + 7z2 + 48 + -33z + -7z2

Combine like terms: 22 + 48 = 70
70 + 22z + -33z + -7z2 = -48 + 33z + 7z2 + 48 + -33z + -7z2

Combine like terms: 22z + -33z = -11z
70 + -11z + -7z2 = -48 + 33z + 7z2 + 48 + -33z + -7z2

Reorder the terms:
70 + -11z + -7z2 = -48 + 48 + 33z + -33z + 7z2 + -7z2

Combine like terms: -48 + 48 = 0
70 + -11z + -7z2 = 0 + 33z + -33z + 7z2 + -7z2
70 + -11z + -7z2 = 33z + -33z + 7z2 + -7z2

Combine like terms: 33z + -33z = 0
70 + -11z + -7z2 = 0 + 7z2 + -7z2
70 + -11z + -7z2 = 7z2 + -7z2

Combine like terms: 7z2 + -7z2 = 0
70 + -11z + -7z2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-10 + 1.571428571z + z2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 1.571428571z + 10 + z2 = 0 + 10

Reorder the terms:
-10 + 10 + 1.571428571z + z2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 1.571428571z + z2 = 0 + 10
1.571428571z + z2 = 0 + 10

Combine like terms: 0 + 10 = 10
1.571428571z + z2 = 10

The z term is 1.571428571z.  Take half its coefficient (0.7857142855).
Square it (0.6173469384) and add it to both sides.

Add '0.6173469384' to each side of the equation.
1.571428571z + 0.6173469384 + z2 = 10 + 0.6173469384

Reorder the terms:
0.6173469384 + 1.571428571z + z2 = 10 + 0.6173469384

Combine like terms: 10 + 0.6173469384 = 10.6173469384
0.6173469384 + 1.571428571z + z2 = 10.6173469384

Factor a perfect square on the left side:
(z + 0.7857142855)(z + 0.7857142855) = 10.6173469384

Calculate the square root of the right side: 3.258427065

Break this problem into two subproblems by setting 
(z + 0.7857142855) equal to 3.258427065 and -3.258427065.

Subproblem 1

z + 0.7857142855 = 3.258427065 Simplifying z + 0.7857142855 = 3.258427065 Reorder the terms: 0.7857142855 + z = 3.258427065 Solving 0.7857142855 + z = 3.258427065 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + z = 3.258427065 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + z = 3.258427065 + -0.7857142855 z = 3.258427065 + -0.7857142855 Combine like terms: 3.258427065 + -0.7857142855 = 2.4727127795 z = 2.4727127795 Simplifying z = 2.4727127795

Subproblem 2

z + 0.7857142855 = -3.258427065 Simplifying z + 0.7857142855 = -3.258427065 Reorder the terms: 0.7857142855 + z = -3.258427065 Solving 0.7857142855 + z = -3.258427065 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + z = -3.258427065 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + z = -3.258427065 + -0.7857142855 z = -3.258427065 + -0.7857142855 Combine like terms: -3.258427065 + -0.7857142855 = -4.0441413505 z = -4.0441413505 Simplifying z = -4.0441413505

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.4727127795, -4.0441413505}

See similar equations:

| 27=9(y-3)+3y+y^2 | | x--2=-7 | | 7/5*x=119 | | 3-5.30x-2.50x=55.20 | | -2x=-x+48 | | 3x+14=7x-23 | | (x+7)(x-1)=x^2+1 | | 195x^2-16x=87 | | 18-6a=4a-4(a+4) | | b+0.6=2 | | 6=-7p | | (3x^2)+5x-1=0 | | 2x*0= | | 4x+6+7x-3=180 | | 308-144x+21x^2-x^3=0 | | (.067)y+7=25 | | 35=-r/5 | | (-7i)(2i)= | | 7x+2-5(x-1)=9x+3 | | 4x-(7x+7)=4x-21 | | 24x^2-6x-12=0 | | v^2+25=36 | | 25y-20+4y-3=180 | | 76=-n-35 | | 11/6x=-1 | | 70c+20=200 | | -140/10 | | r-2(r-1)=5r-5 | | 1+5n=7n+7 | | yp-yz=t | | Ax+3x+bx=-5x+12x | | 3-5=8x+7 |

Equations solver categories