-4z^2+6z+1=0

Simple and best practice solution for -4z^2+6z+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 -4z^2+6z+1=0 equation:


Simplifying
-4z2 + 6z + 1 = 0

Reorder the terms:
1 + 6z + -4z2 = 0

Solving
1 + 6z + -4z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -1.5z + z2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.5z + 0.25 + z2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.5z + z2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.5z + z2 = 0 + 0.25
-1.5z + z2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.5z + z2 = 0.25

The z term is -1.5z.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5z + 0.5625 + z2 = 0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5z + z2 = 0.25 + 0.5625

Combine like terms: 0.25 + 0.5625 = 0.8125
0.5625 + -1.5z + z2 = 0.8125

Factor a perfect square on the left side:
(z + -0.75)(z + -0.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(z + -0.75) equal to 0.901387819 and -0.901387819.

Subproblem 1

z + -0.75 = 0.901387819 Simplifying z + -0.75 = 0.901387819 Reorder the terms: -0.75 + z = 0.901387819 Solving -0.75 + z = 0.901387819 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + z = 0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + z = 0.901387819 + 0.75 z = 0.901387819 + 0.75 Combine like terms: 0.901387819 + 0.75 = 1.651387819 z = 1.651387819 Simplifying z = 1.651387819

Subproblem 2

z + -0.75 = -0.901387819 Simplifying z + -0.75 = -0.901387819 Reorder the terms: -0.75 + z = -0.901387819 Solving -0.75 + z = -0.901387819 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + z = -0.901387819 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + z = -0.901387819 + 0.75 z = -0.901387819 + 0.75 Combine like terms: -0.901387819 + 0.75 = -0.151387819 z = -0.151387819 Simplifying z = -0.151387819

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.651387819, -0.151387819}

See similar equations:

| 3x(x-6)=6x-90 | | -12x+14=-6x+8 | | 4/2=x/7 | | 9(c-4)+5=3+c-34 | | m/8=10/2 | | 4y=x^2+4x | | -9=-8(1+6y)-1 | | 8f=7f+-3 | | 3/6=p-6/p-4 | | (10x-9)-(-x^2+22x)= | | -3x^2=8-10x | | 12(a-9)=-7-5 | | 3lnx-2ln(5-x)=0 | | 20x+4y=-60 | | 2.5x+3=y | | 0.074*n=74 | | r-3/3=r-3/6 | | 2x+-4=-3+7 | | 14+7m-14=28-14 | | 2(x-3)-6x=11-18 | | -[9x(2x+6)]=-3-[4(3x-4)-3x] | | 9+6n=6n^2 | | 10/2=x+1/3 | | n-(12-n)=38 | | n*5.06=506.00 | | x^2+y^2-4x-8y+20=0 | | y-2=-4(x-1) | | 20-2p=5+3p | | .83333333333333333x-3=.625x+7 | | v+5/4=3/6 | | -2(3n-6)=-6 | | 2330100+x=2.1*(863000+x) |

Equations solver categories