z^2+5z=3

Simple and best practice solution for z^2+5z=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+5z=3 equation:


Simplifying
z2 + 5z = 3

Reorder the terms:
5z + z2 = 3

Solving
5z + z2 = 3

Solving for variable 'z'.

Reorder the terms:
-3 + 5z + z2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 5z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 5z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5z + z2 = 0 + 3
5z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
5z + z2 = 3

The z term is 5z.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5z + 6.25 + z2 = 3 + 6.25

Reorder the terms:
6.25 + 5z + z2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + 5z + z2 = 9.25

Factor a perfect square on the left side:
(z + 2.5)(z + 2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(z + 2.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

z + 2.5 = 3.041381265 Simplifying z + 2.5 = 3.041381265 Reorder the terms: 2.5 + z = 3.041381265 Solving 2.5 + z = 3.041381265 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = 3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = 3.041381265 + -2.5 z = 3.041381265 + -2.5 Combine like terms: 3.041381265 + -2.5 = 0.541381265 z = 0.541381265 Simplifying z = 0.541381265

Subproblem 2

z + 2.5 = -3.041381265 Simplifying z + 2.5 = -3.041381265 Reorder the terms: 2.5 + z = -3.041381265 Solving 2.5 + z = -3.041381265 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + z = -3.041381265 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + z = -3.041381265 + -2.5 z = -3.041381265 + -2.5 Combine like terms: -3.041381265 + -2.5 = -5.541381265 z = -5.541381265 Simplifying z = -5.541381265

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.541381265, -5.541381265}

See similar equations:

| y=-5x^2-26x-5 | | 3a^2+4a-1=0 | | 4+3/4= | | 9a^2+12a-3=0 | | y=1+-7x | | -88=-4x+8+20x | | 2y+3=3(3+y) | | 60=-3(7+x)-5(x-5) | | x^2+36=2x | | 7x+18x-54=71 | | (x^2+12x)+(y^2+2y)=-28 | | 8a^2+2a-15=0 | | 4x^4-10x^2-15x=0 | | 6x+2343f=79 | | -13t=-2 | | 2+6p=-6(6+5p)+2 | | -142-20+11x=80 | | 35=5*h*7 | | -6x+16=-62 | | 8a^2-2a-15=0 | | 8a^2+3a-15=0 | | 5*a-4=3*a+2 | | 4+6x=-5(x+4)+7x | | 7(5+7x)=8x-6 | | 8a^2+3a-5=0 | | 5x^2-26x+63=0 | | 7(g+3)=35 | | 5(9x-4)=24 | | 147=3(1-6m) | | 5(e+6)=40 | | 2np-6nq-8n-2=-10p-8 | | 3(a+5)=36 |

Equations solver categories