z^2+10z+11=0

Simple and best practice solution for z^2+10z+11=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+10z+11=0 equation:


Simplifying
z2 + 10z + 11 = 0

Reorder the terms:
11 + 10z + z2 = 0

Solving
11 + 10z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + 10z + -11 + z2 = 0 + -11

Reorder the terms:
11 + -11 + 10z + z2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 10z + z2 = 0 + -11
10z + z2 = 0 + -11

Combine like terms: 0 + -11 = -11
10z + z2 = -11

The z term is 10z.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10z + 25 + z2 = -11 + 25

Reorder the terms:
25 + 10z + z2 = -11 + 25

Combine like terms: -11 + 25 = 14
25 + 10z + z2 = 14

Factor a perfect square on the left side:
(z + 5)(z + 5) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(z + 5) equal to 3.741657387 and -3.741657387.

Subproblem 1

z + 5 = 3.741657387 Simplifying z + 5 = 3.741657387 Reorder the terms: 5 + z = 3.741657387 Solving 5 + z = 3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = 3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + z = 3.741657387 + -5 z = 3.741657387 + -5 Combine like terms: 3.741657387 + -5 = -1.258342613 z = -1.258342613 Simplifying z = -1.258342613

Subproblem 2

z + 5 = -3.741657387 Simplifying z + 5 = -3.741657387 Reorder the terms: 5 + z = -3.741657387 Solving 5 + z = -3.741657387 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + z = -3.741657387 + -5 Combine like terms: 5 + -5 = 0 0 + z = -3.741657387 + -5 z = -3.741657387 + -5 Combine like terms: -3.741657387 + -5 = -8.741657387 z = -8.741657387 Simplifying z = -8.741657387

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-1.258342613, -8.741657387}

See similar equations:

| 5(x+6)+1=3-2x | | 5(6m+7)=-2-7m | | s-9/10=21/10 | | 2(3w-12+w)=640 | | -9p=-72 | | 1.96x^5-4x^2-16x-16=0 | | 7-7(1-7x)=8x | | p(x)=-2x+100x-25 | | s-7/10=13/10 | | 12y=13.2 | | 5x+1+3=8(3x+2)+7(2-3x) | | 7(2y+1)=3(7+5y) | | X+x+.11+x+.11+.38=10.32 | | (2x+10)=(2x-15) | | 2(w+20+w)=380 | | -(1+6n)=-152 | | 121=0 | | 18-[2+3(8-5)]= | | 8(2+2x)-6=90 | | (x-2)2+(y+6)2=25 | | 2(x-3)+9=2x+2 | | X+5x+13=140 | | 1/2x=121 | | 19-5x/2=33 | | Y=6(6)-2 | | -x^2+5x+3=0 | | Y=6(4)-2 | | -4z+6x-2y+2z-3y= | | 3x/4x-2-2x/6x-3=5/2x-1 | | 14x+4+18x-4+14x-8=360 | | (6x-9)(3x+4)=0 | | 5/6=x/32 |

Equations solver categories