0=z^2-26z+100

Simple and best practice solution for 0=z^2-26z+100 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 0=z^2-26z+100 equation:


Simplifying
0 = z2 + -26z + 100

Reorder the terms:
0 = 100 + -26z + z2

Solving
0 = 100 + -26z + z2

Solving for variable 'z'.

Combine like terms: 0 + -100 = -100
-100 + 26z + -1z2 = 100 + -26z + z2 + -100 + 26z + -1z2

Reorder the terms:
-100 + 26z + -1z2 = 100 + -100 + -26z + 26z + z2 + -1z2

Combine like terms: 100 + -100 = 0
-100 + 26z + -1z2 = 0 + -26z + 26z + z2 + -1z2
-100 + 26z + -1z2 = -26z + 26z + z2 + -1z2

Combine like terms: -26z + 26z = 0
-100 + 26z + -1z2 = 0 + z2 + -1z2
-100 + 26z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-100 + 26z + -1z2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
100 + -26z + z2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -26z + -100 + z2 = 0 + -100

Reorder the terms:
100 + -100 + -26z + z2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -26z + z2 = 0 + -100
-26z + z2 = 0 + -100

Combine like terms: 0 + -100 = -100
-26z + z2 = -100

The z term is -26z.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26z + 169 + z2 = -100 + 169

Reorder the terms:
169 + -26z + z2 = -100 + 169

Combine like terms: -100 + 169 = 69
169 + -26z + z2 = 69

Factor a perfect square on the left side:
(z + -13)(z + -13) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(z + -13) equal to 8.306623863 and -8.306623863.

Subproblem 1

z + -13 = 8.306623863 Simplifying z + -13 = 8.306623863 Reorder the terms: -13 + z = 8.306623863 Solving -13 + z = 8.306623863 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + z = 8.306623863 + 13 Combine like terms: -13 + 13 = 0 0 + z = 8.306623863 + 13 z = 8.306623863 + 13 Combine like terms: 8.306623863 + 13 = 21.306623863 z = 21.306623863 Simplifying z = 21.306623863

Subproblem 2

z + -13 = -8.306623863 Simplifying z + -13 = -8.306623863 Reorder the terms: -13 + z = -8.306623863 Solving -13 + z = -8.306623863 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + z = -8.306623863 + 13 Combine like terms: -13 + 13 = 0 0 + z = -8.306623863 + 13 z = -8.306623863 + 13 Combine like terms: -8.306623863 + 13 = 4.693376137 z = 4.693376137 Simplifying z = 4.693376137

Solution

The solution to the problem is based on the solutions from the subproblems. z = {21.306623863, 4.693376137}

See similar equations:

| 6v-v=25 | | 8+4(2x+10)=24 | | 9/26=n/52 | | y=3x^2-30x+69 | | 3n+23=36 | | (5/2)(4x-8)-2(6x-7)=-10 | | 3x+5x-15=6x-1 | | 360=z+55+78+74 | | 25/4=n/12 | | 15x+3=15x-10 | | x^2+10x=4x^2-8 | | 360=2+55+78+74 | | 3b*7n= | | 3x+5x-15=6sx-1 | | 40=((x-0.1)/x)*100 | | x^5-6x^3+9t=0 | | x+1=3x-8 | | x^2+10=4x^2-8 | | 4x-y+15=0 | | 17-k=2 | | 360=(z+45)+2+55+78+74 | | ​(10-​5*​y/​2) | | X=506/x-1 | | 4x-7/3= | | 5*​(20-​3*​(10-​5*​y/​2)) | | -4.9x^2+14.7x+58.8=0 | | X+x+6=41 | | 7(41x-9)=-26+6x | | -4(-3x-3)-x+3=59 | | Y=-16r^2+224 | | 6y=y+33 | | 7-u=17 |

Equations solver categories