z^2+4z=2

Simple and best practice solution for z^2+4z=2 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 z^2+4z=2 equation:


Simplifying
z2 + 4z = 2

Reorder the terms:
4z + z2 = 2

Solving
4z + z2 = 2

Solving for variable 'z'.

Reorder the terms:
-2 + 4z + z2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 4z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4z + 2 + z2 = 0 + 2

Reorder the terms:
-2 + 2 + 4z + z2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4z + z2 = 0 + 2
4z + z2 = 0 + 2

Combine like terms: 0 + 2 = 2
4z + z2 = 2

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 = 2 + 4

Reorder the terms:
4 + 4z + z2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + 4z + z2 = 6

Factor a perfect square on the left side:
(z + 2)(z + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(z + 2) equal to 2.449489743 and -2.449489743.

Subproblem 1

z + 2 = 2.449489743 Simplifying z + 2 = 2.449489743 Reorder the terms: 2 + z = 2.449489743 Solving 2 + z = 2.449489743 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 = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + z = 2.449489743 + -2 z = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 z = 0.449489743 Simplifying z = 0.449489743

Subproblem 2

z + 2 = -2.449489743 Simplifying z + 2 = -2.449489743 Reorder the terms: 2 + z = -2.449489743 Solving 2 + z = -2.449489743 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 = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + z = -2.449489743 + -2 z = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 z = -4.449489743 Simplifying z = -4.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.449489743, -4.449489743}

See similar equations:

| 5(g-6)+g=6(g-4) | | 1/8v=1/4 | | 3(2+4)-5= | | -7(v+3)+4v+7=8v+8 | | 3-x=5x+15 | | 2x^2-5x+2=(x+3)(x-2)+3x | | -x+7=5x+1 | | -14/2*4 | | -b+3-1=3.4 | | -7(1-4b)+2=-201 | | 84-5x=31x+20 | | 2t+5=5t-1 | | y+10=y/5+36/5-2/3 | | 3000*12= | | -1-(-3)=0 | | 2m-6(5-7m)=-382 | | 1/5+m=2/5 | | 5x+11=2x+2 | | 3y+5+2y=5(2y+1) | | 3(5+7m)=6m+30 | | x+(x-5)=43 | | -75-10x=43-24x | | 8x+7=13+7x | | 180=16t^2 | | -2x+-9=15 | | 8x^2+3x+2=-11 | | .75(a-35.8)=a-22.4 | | 20=2(2x+8) | | -31=-6+5x | | 8-2h=5 | | 4u+2=6 | | 5(n-1)=40 |

Equations solver categories