z^2+14z+10=

Simple and best practice solution for z^2+14z+10= 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+14z+10= equation:


Simplifying
z2 + 14z + 10 = 0

Reorder the terms:
10 + 14z + z2 = 0

Solving
10 + 14z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 14z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + 14z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 14z + z2 = 0 + -10
14z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
14z + z2 = -10

The z term is 14z.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14z + 49 + z2 = -10 + 49

Reorder the terms:
49 + 14z + z2 = -10 + 49

Combine like terms: -10 + 49 = 39
49 + 14z + z2 = 39

Factor a perfect square on the left side:
(z + 7)(z + 7) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(z + 7) equal to 6.244997998 and -6.244997998.

Subproblem 1

z + 7 = 6.244997998 Simplifying z + 7 = 6.244997998 Reorder the terms: 7 + z = 6.244997998 Solving 7 + z = 6.244997998 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = 6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + z = 6.244997998 + -7 z = 6.244997998 + -7 Combine like terms: 6.244997998 + -7 = -0.755002002 z = -0.755002002 Simplifying z = -0.755002002

Subproblem 2

z + 7 = -6.244997998 Simplifying z + 7 = -6.244997998 Reorder the terms: 7 + z = -6.244997998 Solving 7 + z = -6.244997998 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + z = -6.244997998 + -7 Combine like terms: 7 + -7 = 0 0 + z = -6.244997998 + -7 z = -6.244997998 + -7 Combine like terms: -6.244997998 + -7 = -13.244997998 z = -13.244997998 Simplifying z = -13.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.755002002, -13.244997998}

See similar equations:

| 8.91x+35.64=71.28 | | 5e-9=-99 | | 6(x+3)=6x+8 | | 4ln(x)+5=-1 | | -1=-3-4x-6 | | (6y+5+2)+8(y+1)= | | 5x-24=8x | | 3x+11+2x=2(x+11)+3 | | 33+p=5(4p-1) | | x-.10=562.5 | | x+0.15x=1 | | 3r-5=-128 | | 20+7b=-20+19b-20 | | 3+8x=3(2x+-1) | | 9x+-4x=20 | | -5m-25=0 | | 9x+30=4x-6 | | 249=4b+7(-6+3) | | 3(2m+2)-2(m-4)=6 | | x-10x=562.5 | | 8b+8b=27 | | 5m-25=0 | | 10-4(8+7)=2(1-p) | | -6n-3=-27 | | (5x-8)=5x-(8+2) | | 5y-7y=48+y | | x^2+33x+270=0 | | 9x-6=-51 | | 4x+5(2-x)=16 | | Log[5](2x-1)+Log[5](x-1)=1 | | -5(7x-6)=-35x+30 | | -7+-2y+2y=-7 |

Equations solver categories