z^2+1z=3

Simple and best practice solution for z^2+1z=3 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+1z=3 equation:


Simplifying
z2 + 1z = 3

Reorder the terms:
1z + z2 = 3

Solving
1z + z2 = 3

Solving for variable 'z'.

Reorder the terms:
-3 + 1z + z2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 1z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1z + z2 = 0 + 3
1z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
1z + z2 = 3

The z term is 1z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = 3 + 0.25

Reorder the terms:
0.25 + z + z2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
0.25 + z + z2 = 3.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(z + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

z + 0.5 = 1.802775638 Simplifying z + 0.5 = 1.802775638 Reorder the terms: 0.5 + z = 1.802775638 Solving 0.5 + z = 1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 1.802775638 + -0.5 z = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 z = 1.302775638 Simplifying z = 1.302775638

Subproblem 2

z + 0.5 = -1.802775638 Simplifying z + 0.5 = -1.802775638 Reorder the terms: 0.5 + z = -1.802775638 Solving 0.5 + z = -1.802775638 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + z = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -1.802775638 + -0.5 z = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 z = -2.302775638 Simplifying z = -2.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.302775638, -2.302775638}

See similar equations:

| 5(4r-8)=38+7N | | 4-2(x+3)+1=3 | | -3(x-7)-(-4x+5)=-6x+8x | | 6X^3+5x^2-104x-180=0 | | -g=-40 | | 735.95-15.95=12x | | 3(3y+5)-4y=-5 | | (-5x)+(-2)=(-2x)+4 | | 455=3x+1.5x+x | | -c+A+b=180 | | -(-3b-4)=4(3b-8) | | 70+-5x=20 | | 3n-1=n+4+n | | -8i(20i-13)= | | -4(-8x-8)+7(7-2x)=(16+19x) | | 5x+8x-2x-5=6 | | 9+5=4t | | 9i-(10-8i)= | | 1-10(63-4b)=b-2 | | 2x+-12=-20-y | | 3n-3(3n-6)=20 | | 52=410 | | =X^2(2x-5)-31 | | 5*x+6=10 | | a-4b-3c+2d=0 | | n+7-6n=-6(n-8)-6(n-6) | | 0.2x-12=70 | | 32c-23-14c-31= | | =X^2(2x-5) | | 45+4x=61+2c | | -6v+4(2v-5)=-(-2v-7) | | 4a=1+13 |

Equations solver categories