z^2-z-0.5=0

Simple and best practice solution for z^2-z-0.5=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 z^2-z-0.5=0 equation:


Simplifying
z2 + -1z + -0.5 = 0

Reorder the terms:
-0.5 + -1z + z2 = 0

Solving
-0.5 + -1z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1z + 0.5 + z2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1z + z2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1z + z2 = 0 + 0.5
-1z + z2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1z + z2 = 0.5

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.
-1z + 0.25 + z2 = 0.5 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1z + z2 = 0.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(z + -0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

z + -0.5 = 0.866025404 Simplifying z + -0.5 = 0.866025404 Reorder the terms: -0.5 + z = 0.866025404 Solving -0.5 + z = 0.866025404 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 = 0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 0.866025404 + 0.5 z = 0.866025404 + 0.5 Combine like terms: 0.866025404 + 0.5 = 1.366025404 z = 1.366025404 Simplifying z = 1.366025404

Subproblem 2

z + -0.5 = -0.866025404 Simplifying z + -0.5 = -0.866025404 Reorder the terms: -0.5 + z = -0.866025404 Solving -0.5 + z = -0.866025404 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 = -0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -0.866025404 + 0.5 z = -0.866025404 + 0.5 Combine like terms: -0.866025404 + 0.5 = -0.366025404 z = -0.366025404 Simplifying z = -0.366025404

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.366025404, -0.366025404}

See similar equations:

| 15+2n=11 | | (2y^2)(2y^2)= | | 2(3d+7)=5+6f | | 8(x-3)=6x+6 | | z^2+z+0.5=0 | | 112+6x=70 | | 5n^2+n-7=-3 | | 3(6x-5)-7(3x+10)=0 | | 3x^2+11x-10=0 | | x+.07x=50.54 | | 2(x-2)+(x+2)=6 | | 5n^2+-7=-3 | | 4a^2=6 | | 6(z+9)-6q=4(6z-8) | | 8xsin(8x)=0 | | 2(3(1.5)-4)=8(1.5)-11 | | 5x+x(squared)=120 | | 6x+9y+4xz+6yz=2x+3y | | 3x-2+3*6x=2-2x+2 | | 0=-16t^2+320t+32 | | 13+4(x+9)=104 | | 4t-7=2t-1 | | 8t-18=3(t-6)+5t | | 9g^2-7g-4= | | (4x^5+3x-12)-(3x^3+x^2-3x-6)= | | 6x+5+5(2+x)= | | 12=x*(2x-5) | | 2*-28+3y=-59 | | 4x(10x+1)=0 | | 6w^2+25W+21=0 | | 5a+2-7=0 | | 2*-28+3y=4 |

Equations solver categories