1+7z+z^2=0

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


Simplifying
1 + 7z + z2 = 0

Solving
1 + 7z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 7z + -1 + z2 = 0 + -1

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

Combine like terms: 1 + -1 = 0
0 + 7z + z2 = 0 + -1
7z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
7z + z2 = -1

The z term is 7z.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7z + 12.25 + z2 = -1 + 12.25

Reorder the terms:
12.25 + 7z + z2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + 7z + z2 = 11.25

Factor a perfect square on the left side:
(z + 3.5)(z + 3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(z + 3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

z + 3.5 = 3.354101966 Simplifying z + 3.5 = 3.354101966 Reorder the terms: 3.5 + z = 3.354101966 Solving 3.5 + z = 3.354101966 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + z = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + z = 3.354101966 + -3.5 z = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 z = -0.145898034 Simplifying z = -0.145898034

Subproblem 2

z + 3.5 = -3.354101966 Simplifying z + 3.5 = -3.354101966 Reorder the terms: 3.5 + z = -3.354101966 Solving 3.5 + z = -3.354101966 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + z = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + z = -3.354101966 + -3.5 z = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 z = -6.854101966 Simplifying z = -6.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.145898034, -6.854101966}

See similar equations:

| -6p-3(6-4p)=4(p-4)16 | | 2=x^2+0.5x | | .25q+2=(-6q+3)4(2q+1) | | .25q+2=-6q+4(2q+1) | | -x^2+2x+18=5x-10 | | 5*y-50=y | | 13p+4(3p-12)=-19.8125 | | 14+26x=28+19x | | -20=-4u | | (x^2)+-11x+10=0 | | (3x+y)(x-6y)= | | 5+6x=10+2x | | 6w+v^2x=y | | -2.75q=9 | | x+2(-1)=3 | | 7(-k-8)=-32+k | | ln(x)=0.095*x | | 25+5x=135 | | 3-2y-y=6 | | 7y=8-5x | | 900-240x+12x^2=0 | | 7(5x+6)+(x+5)=23 | | -25=5w | | -12=3x-5x+4 | | (-3x^4-9x^3-4x^2+4)+(8x^3-7x^3-7x^3-x-6)= | | -9(3x+15)=-36x-32 | | Cx+Fy=J | | 7A+3B=43 | | (5x+4)(3x-2)= | | 2x-2-x=6 | | Y=-8+4x | | 4x^2+24x+17=0 |

Equations solver categories