3z^2+95z+12=0

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Solution for 3z^2+95z+12=0 equation:


Simplifying
3z2 + 95z + 12 = 0

Reorder the terms:
12 + 95z + 3z2 = 0

Solving
12 + 95z + 3z2 = 0

Solving for variable 'z'.

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

Divide each side by '3'.
4 + 31.66666667z + z2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 31.66666667z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 31.66666667z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 31.66666667z + z2 = 0 + -4
31.66666667z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
31.66666667z + z2 = -4

The z term is 31.66666667z.  Take half its coefficient (15.83333334).
Square it (250.6944447) and add it to both sides.

Add '250.6944447' to each side of the equation.
31.66666667z + 250.6944447 + z2 = -4 + 250.6944447

Reorder the terms:
250.6944447 + 31.66666667z + z2 = -4 + 250.6944447

Combine like terms: -4 + 250.6944447 = 246.6944447
250.6944447 + 31.66666667z + z2 = 246.6944447

Factor a perfect square on the left side:
(z + 15.83333334)(z + 15.83333334) = 246.6944447

Calculate the square root of the right side: 15.706509628

Break this problem into two subproblems by setting 
(z + 15.83333334) equal to 15.706509628 and -15.706509628.

Subproblem 1

z + 15.83333334 = 15.706509628 Simplifying z + 15.83333334 = 15.706509628 Reorder the terms: 15.83333334 + z = 15.706509628 Solving 15.83333334 + z = 15.706509628 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15.83333334' to each side of the equation. 15.83333334 + -15.83333334 + z = 15.706509628 + -15.83333334 Combine like terms: 15.83333334 + -15.83333334 = 0.00000000 0.00000000 + z = 15.706509628 + -15.83333334 z = 15.706509628 + -15.83333334 Combine like terms: 15.706509628 + -15.83333334 = -0.126823712 z = -0.126823712 Simplifying z = -0.126823712

Subproblem 2

z + 15.83333334 = -15.706509628 Simplifying z + 15.83333334 = -15.706509628 Reorder the terms: 15.83333334 + z = -15.706509628 Solving 15.83333334 + z = -15.706509628 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15.83333334' to each side of the equation. 15.83333334 + -15.83333334 + z = -15.706509628 + -15.83333334 Combine like terms: 15.83333334 + -15.83333334 = 0.00000000 0.00000000 + z = -15.706509628 + -15.83333334 z = -15.706509628 + -15.83333334 Combine like terms: -15.706509628 + -15.83333334 = -31.539842968 z = -31.539842968 Simplifying z = -31.539842968

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.126823712, -31.539842968}

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