z^2+12z-25=0

Simple and best practice solution for z^2+12z-25=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+12z-25=0 equation:


Simplifying
z2 + 12z + -25 = 0

Reorder the terms:
-25 + 12z + z2 = 0

Solving
-25 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 12z + 25 + z2 = 0 + 25

Reorder the terms:
-25 + 25 + 12z + z2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 12z + z2 = 0 + 25
12z + z2 = 0 + 25

Combine like terms: 0 + 25 = 25
12z + z2 = 25

The z term is 12z.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12z + 36 + z2 = 25 + 36

Reorder the terms:
36 + 12z + z2 = 25 + 36

Combine like terms: 25 + 36 = 61
36 + 12z + z2 = 61

Factor a perfect square on the left side:
(z + 6)(z + 6) = 61

Calculate the square root of the right side: 7.810249676

Break this problem into two subproblems by setting 
(z + 6) equal to 7.810249676 and -7.810249676.

Subproblem 1

z + 6 = 7.810249676 Simplifying z + 6 = 7.810249676 Reorder the terms: 6 + z = 7.810249676 Solving 6 + z = 7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 7.810249676 + -6 Combine like terms: 6 + -6 = 0 0 + z = 7.810249676 + -6 z = 7.810249676 + -6 Combine like terms: 7.810249676 + -6 = 1.810249676 z = 1.810249676 Simplifying z = 1.810249676

Subproblem 2

z + 6 = -7.810249676 Simplifying z + 6 = -7.810249676 Reorder the terms: 6 + z = -7.810249676 Solving 6 + z = -7.810249676 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = -7.810249676 + -6 Combine like terms: 6 + -6 = 0 0 + z = -7.810249676 + -6 z = -7.810249676 + -6 Combine like terms: -7.810249676 + -6 = -13.810249676 z = -13.810249676 Simplifying z = -13.810249676

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.810249676, -13.810249676}

See similar equations:

| (6x^3+7x+12)-(3x^2+8x+8)= | | -3+2x=19 | | 2z-31=9z+21 | | 9x+5=77 | | 15x+5=85 | | -1+2x=7 | | y^2+6y-15=0 | | 3a^2-6a+3=0 | | 3-10b=2-9 | | 18x+25=123 | | 3.5m=182 | | ln(x+8)+ln(x+2)=3 | | 14x+25=115 | | 2(b+6)+4b=376 | | 9d-27=36 | | 5x-y=13 | | -3(6x+8)=-24 | | 15*2-34x+15=0 | | 7(7c+1)-4c=13(c-2)+3 | | 2x^2-5y^2=7 | | 10-4x=193 | | 14w=91 | | 1d+(1d*4-12)=(1d*3) | | 4(x+y+z)=xyz | | 4x=7y+10 | | T-66=-55 | | 6(2x+2)=108 | | 5x^4-12x^3=0 | | 14-3(5m-12)=1-(20m+1) | | 15x^5y+35x^3y^3= | | 10+x=50 | | 2u=26 |

Equations solver categories