z^2-14z=-9

Simple and best practice solution for z^2-14z=-9 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=-9 equation:


Simplifying
z2 + -14z = -9

Reorder the terms:
-14z + z2 = -9

Solving
-14z + z2 = -9

Solving for variable 'z'.

Reorder the terms:
9 + -14z + z2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -14z + -9 + z2 = 0 + -9

Reorder the terms:
9 + -9 + -14z + z2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -14z + z2 = 0 + -9
-14z + z2 = 0 + -9

Combine like terms: 0 + -9 = -9
-14z + z2 = -9

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 = -9 + 49

Reorder the terms:
49 + -14z + z2 = -9 + 49

Combine like terms: -9 + 49 = 40
49 + -14z + z2 = 40

Factor a perfect square on the left side:
(z + -7)(z + -7) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(z + -7) equal to 6.32455532 and -6.32455532.

Subproblem 1

z + -7 = 6.32455532 Simplifying z + -7 = 6.32455532 Reorder the terms: -7 + z = 6.32455532 Solving -7 + z = 6.32455532 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 = 6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + z = 6.32455532 + 7 z = 6.32455532 + 7 Combine like terms: 6.32455532 + 7 = 13.32455532 z = 13.32455532 Simplifying z = 13.32455532

Subproblem 2

z + -7 = -6.32455532 Simplifying z + -7 = -6.32455532 Reorder the terms: -7 + z = -6.32455532 Solving -7 + z = -6.32455532 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 = -6.32455532 + 7 Combine like terms: -7 + 7 = 0 0 + z = -6.32455532 + 7 z = -6.32455532 + 7 Combine like terms: -6.32455532 + 7 = 0.67544468 z = 0.67544468 Simplifying z = 0.67544468

Solution

The solution to the problem is based on the solutions from the subproblems. z = {13.32455532, 0.67544468}

See similar equations:

| 22c+5=60 | | x^2+2.5x+1.56=2 | | 10w-6=9w+1 | | 5n^2-2n-10=15 | | 6x^2=96 | | x+11=2z+8 | | X^2+2n+4=0 | | 6p=7(5p+7) | | 2.03y+3.8=-0.26 | | (x-4)(x+5)=-3(x-4) | | 12=.5x(x+(2x)) | | (5x)+16=500 | | 4w-2=-10 | | 4a-3a+2a=24 | | (5x)16=500 | | 6x+5y=57 | | 4n^2-3n-8=12 | | -28=5y+7 | | 20x^2-20x+5=0 | | 0.8-c=0.8 | | x^2+6ax=0 | | g(-1)=-x+1 | | -5t^2+7t-2=0 | | 3(q-3)=4(3-4q) | | 2x+2(x+3)=2(x+7) | | 12x^2-129x-33=0 | | 2.5(1.9)+4.3(7.3)= | | 3b^2+4b+1=0 | | 7p-2p=8-3p | | 7a-2=8-3a | | 16x^2-9x+25=-49x | | 14x-(3x-2)=[5x+2-(x-1)] |

Equations solver categories