7z^2-8z-1=0

Simple and best practice solution for 7z^2-8z-1=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 7z^2-8z-1=0 equation:


Simplifying
7z2 + -8z + -1 = 0

Reorder the terms:
-1 + -8z + 7z2 = 0

Solving
-1 + -8z + 7z2 = 0

Solving for variable 'z'.

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

Divide each side by '7'.
-0.1428571429 + -1.142857143z + z2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + -1.142857143z + 0.1428571429 + z2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + -1.142857143z + z2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + -1.142857143z + z2 = 0 + 0.1428571429
-1.142857143z + z2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
-1.142857143z + z2 = 0.1428571429

The z term is -1.142857143z.  Take half its coefficient (-0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
-1.142857143z + 0.3265306123 + z2 = 0.1428571429 + 0.3265306123

Reorder the terms:
0.3265306123 + -1.142857143z + z2 = 0.1428571429 + 0.3265306123

Combine like terms: 0.1428571429 + 0.3265306123 = 0.4693877552
0.3265306123 + -1.142857143z + z2 = 0.4693877552

Factor a perfect square on the left side:
(z + -0.5714285715)(z + -0.5714285715) = 0.4693877552

Calculate the square root of the right side: 0.685118789

Break this problem into two subproblems by setting 
(z + -0.5714285715) equal to 0.685118789 and -0.685118789.

Subproblem 1

z + -0.5714285715 = 0.685118789 Simplifying z + -0.5714285715 = 0.685118789 Reorder the terms: -0.5714285715 + z = 0.685118789 Solving -0.5714285715 + z = 0.685118789 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + z = 0.685118789 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + z = 0.685118789 + 0.5714285715 z = 0.685118789 + 0.5714285715 Combine like terms: 0.685118789 + 0.5714285715 = 1.2565473605 z = 1.2565473605 Simplifying z = 1.2565473605

Subproblem 2

z + -0.5714285715 = -0.685118789 Simplifying z + -0.5714285715 = -0.685118789 Reorder the terms: -0.5714285715 + z = -0.685118789 Solving -0.5714285715 + z = -0.685118789 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.5714285715' to each side of the equation. -0.5714285715 + 0.5714285715 + z = -0.685118789 + 0.5714285715 Combine like terms: -0.5714285715 + 0.5714285715 = 0.0000000000 0.0000000000 + z = -0.685118789 + 0.5714285715 z = -0.685118789 + 0.5714285715 Combine like terms: -0.685118789 + 0.5714285715 = -0.1136902175 z = -0.1136902175 Simplifying z = -0.1136902175

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.2565473605, -0.1136902175}

See similar equations:

| 8x^5=-1000x^2 | | 3-4(t+1)=7 | | 4x^2-3x-22=0 | | 48y^3=3Y | | 2=4(1+z) | | 50b^3+25b^2-18b-9=0 | | (8+w)(w)=100 | | 2x-2(-x+5)=x+(-1) | | 4x-2y-10=0 | | -5z+1=-42 | | 4a-3=28 | | 20=3n-n+6 | | 230-4x=32x+22 | | (4x-2)(x+6)=0 | | 2y^2-5y-12=0 | | 7-10x=72-45x | | 2(x-3)=5(x+2)+2 | | -102-8x=72-45x | | 3m+6-7m=-18 | | x^2-6x-18=0 | | .88*172= | | 6x+29=16x-81 | | [100-12]/100= | | [100-12]/100*172= | | -12=5(p-2) | | 6+22=15x-59 | | logx+log(x+6)=2 | | 2k-5+3k=10 | | 2.3x+4.8=9.3 | | 5x+(7-2x)=-20 | | 2+6x=27+x | | 2x+24=5x+15 |

Equations solver categories