8z+3-2z^2+10z=

Simple and best practice solution for 8z+3-2z^2+10z= 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 8z+3-2z^2+10z= equation:


Simplifying
8z + 3 + -2z2 + 10z = 0

Reorder the terms:
3 + 8z + 10z + -2z2 = 0

Combine like terms: 8z + 10z = 18z
3 + 18z + -2z2 = 0

Solving
3 + 18z + -2z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + -9z + z2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -9z + 1.5 + z2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -9z + z2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -9z + z2 = 0 + 1.5
-9z + z2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-9z + z2 = 1.5

The z term is -9z.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9z + 20.25 + z2 = 1.5 + 20.25

Reorder the terms:
20.25 + -9z + z2 = 1.5 + 20.25

Combine like terms: 1.5 + 20.25 = 21.75
20.25 + -9z + z2 = 21.75

Factor a perfect square on the left side:
(z + -4.5)(z + -4.5) = 21.75

Calculate the square root of the right side: 4.663689527

Break this problem into two subproblems by setting 
(z + -4.5) equal to 4.663689527 and -4.663689527.

Subproblem 1

z + -4.5 = 4.663689527 Simplifying z + -4.5 = 4.663689527 Reorder the terms: -4.5 + z = 4.663689527 Solving -4.5 + z = 4.663689527 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + z = 4.663689527 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = 4.663689527 + 4.5 z = 4.663689527 + 4.5 Combine like terms: 4.663689527 + 4.5 = 9.163689527 z = 9.163689527 Simplifying z = 9.163689527

Subproblem 2

z + -4.5 = -4.663689527 Simplifying z + -4.5 = -4.663689527 Reorder the terms: -4.5 + z = -4.663689527 Solving -4.5 + z = -4.663689527 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + z = -4.663689527 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + z = -4.663689527 + 4.5 z = -4.663689527 + 4.5 Combine like terms: -4.663689527 + 4.5 = -0.163689527 z = -0.163689527 Simplifying z = -0.163689527

Solution

The solution to the problem is based on the solutions from the subproblems. z = {9.163689527, -0.163689527}

See similar equations:

| 6(-5r+-1)= | | Ln(2x+4)=3 | | 8(7x+12)=488 | | 3Q-2(Q+4)=-5Q+2 | | 4x-2=3-1x | | (7u^2-u-2)+(5u^2-6u+3)= | | -8(-3+-6s)= | | 3Q+2(Q-4)=-5Q+2 | | 5x^3-500x=0 | | -5(6j+-9)= | | 2x=5.73 | | 406=7(6x+4) | | 4n-9=-13+8n | | 4Q-2(Q+4)=-5Q+6 | | -5(-1+-3c)= | | 6z-20=-16+2z | | 9(11-8q-2q^2)= | | ln(-4y+8)-ln(y+7)=ln(-12y+13) | | -4(x-3)=-(3x+10) | | 18=3.14x | | 6x^2+10x-3x^2+5x^3= | | -0.2=0.17 | | 18(3.14)=3.14x | | 0.28+=1 | | Cos(pi+x)+cos(pi+x)=1 | | 6(5y+5)= | | x^3+4*x^2+3*x=0 | | 4n-16=4 | | 3.14x=18 | | 7(8w+9)= | | 3d(6b+d^2)= | | 2k^2-kx+48=0 |

Equations solver categories