=z^2+8z-15

Simple and best practice solution for =z^2+8z-15 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+8z-15 equation:


Simplifying
0 = z2 + 8z + -15

Reorder the terms:
0 = -15 + 8z + z2

Solving
0 = -15 + 8z + z2

Solving for variable 'z'.

Combine like terms: 0 + 15 = 15
15 + -8z + -1z2 = -15 + 8z + z2 + 15 + -8z + -1z2

Reorder the terms:
15 + -8z + -1z2 = -15 + 15 + 8z + -8z + z2 + -1z2

Combine like terms: -15 + 15 = 0
15 + -8z + -1z2 = 0 + 8z + -8z + z2 + -1z2
15 + -8z + -1z2 = 8z + -8z + z2 + -1z2

Combine like terms: 8z + -8z = 0
15 + -8z + -1z2 = 0 + z2 + -1z2
15 + -8z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
15 + -8z + -1z2 = 0

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

Divide each side by '-1'.
-15 + 8z + z2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8z + 15 + z2 = 0 + 15

Reorder the terms:
-15 + 15 + 8z + z2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8z + z2 = 0 + 15
8z + z2 = 0 + 15

Combine like terms: 0 + 15 = 15
8z + z2 = 15

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = 15 + 16

Reorder the terms:
16 + 8z + z2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + 8z + z2 = 31

Factor a perfect square on the left side:
(z + 4)(z + 4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(z + 4) equal to 5.567764363 and -5.567764363.

Subproblem 1

z + 4 = 5.567764363 Simplifying z + 4 = 5.567764363 Reorder the terms: 4 + z = 5.567764363 Solving 4 + z = 5.567764363 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + z = 5.567764363 + -4 z = 5.567764363 + -4 Combine like terms: 5.567764363 + -4 = 1.567764363 z = 1.567764363 Simplifying z = 1.567764363

Subproblem 2

z + 4 = -5.567764363 Simplifying z + 4 = -5.567764363 Reorder the terms: 4 + z = -5.567764363 Solving 4 + z = -5.567764363 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -5.567764363 + -4 Combine like terms: 4 + -4 = 0 0 + z = -5.567764363 + -4 z = -5.567764363 + -4 Combine like terms: -5.567764363 + -4 = -9.567764363 z = -9.567764363 Simplifying z = -9.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.567764363, -9.567764363}

See similar equations:

| y=-4-2 | | 6(n+8)=-96 | | 5t^3-9t^2-2t=0 | | w^3+w^2-w+1=0 | | 5x-2+3x=17+2x-23 | | -4.2x=21 | | 2(6+o)=20 | | 57-5x=8x+18 | | w^3+w^2-w+1= | | 63-4t=55 | | 5x-7=13-3x | | 8y^3-2y=0 | | 0.4=8-2.5x | | 6b=14.4 | | x+0.7=-0.6 | | 0.4=8-2.5 | | y=4-2 | | 32+x=109 | | z-45=-12 | | r-19=-48 | | w^2-w-12=0 | | -19-4=13-8 | | 5g+2.3=-18.8 | | 2a^2-4ab+5ab-10b^2=0 | | 2(m+25)=4(m-0.5) | | 13-4n=1-n | | 2(0)-0=4 | | 16x-24x+9=0 | | 3x-6=2x+9 | | 5x+21=2x+72 | | 2(2+0.5y)-y=4 | | -2(4x-3)=2x |

Equations solver categories