2z^2-8z+3=0

Simple and best practice solution for 2z^2-8z+3=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 2z^2-8z+3=0 equation:


Simplifying
2z2 + -8z + 3 = 0

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

Solving
3 + -8z + 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 + -4z + z2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4z + -1.5 + z2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4z + z2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4z + z2 = 0 + -1.5
-4z + z2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4z + z2 = -1.5

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 = -1.5 + 4

Reorder the terms:
4 + -4z + z2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + -4z + z2 = 2.5

Factor a perfect square on the left side:
(z + -2)(z + -2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(z + -2) equal to 1.58113883 and -1.58113883.

Subproblem 1

z + -2 = 1.58113883 Simplifying z + -2 = 1.58113883 Reorder the terms: -2 + z = 1.58113883 Solving -2 + z = 1.58113883 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 = 1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + z = 1.58113883 + 2 z = 1.58113883 + 2 Combine like terms: 1.58113883 + 2 = 3.58113883 z = 3.58113883 Simplifying z = 3.58113883

Subproblem 2

z + -2 = -1.58113883 Simplifying z + -2 = -1.58113883 Reorder the terms: -2 + z = -1.58113883 Solving -2 + z = -1.58113883 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 = -1.58113883 + 2 Combine like terms: -2 + 2 = 0 0 + z = -1.58113883 + 2 z = -1.58113883 + 2 Combine like terms: -1.58113883 + 2 = 0.41886117 z = 0.41886117 Simplifying z = 0.41886117

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.58113883, 0.41886117}

See similar equations:

| 7B/16+5 | | -8(2x-1)=40 | | -24+7= | | 0.4x-0.2=-.12 | | 108+4u=-2n | | 6f+12=6f+12 | | 7x+11x=14a | | (x+4)=(2x-9) | | 29(x)=11x+36 | | 7(8+7k)=8k+15 | | -105+4x=-9x+77 | | m+(-2)=-17 | | M^(2/3)-2m^(1/3)-8 | | 4(y+1)=6y-1 | | -81=-3a | | -4v+2(-2v-7)=-28+6v | | 4.9t^2-8t=60 | | 5m-25=-31+-7m | | 12x-8y=16 | | 10y+1=-2+4y | | 2c+2=2 | | X+9=17/2 | | 4y-28=y+13 | | X+(x+2)=100 | | 9-(n-5)=30 | | 6/F=0.2 | | 8z=5z-30 | | 7x^2=x-8 | | -4(5-7e)= | | -7x(2x-1)=4(2x+1) | | 4m-29=-8+m | | -2(5x+3)= |

Equations solver categories