-4z^2+6z+5=0

Simple and best practice solution for -4z^2+6z+5=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+5=0 equation:


Simplifying
-4z2 + 6z + 5 = 0

Reorder the terms:
5 + 6z + -4z2 = 0

Solving
5 + 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'.
-1.25 + -1.5z + z2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.5z + 1.25 + z2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.5z + z2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.5z + z2 = 0 + 1.25
-1.5z + z2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.5z + z2 = 1.25

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 = 1.25 + 0.5625

Reorder the terms:
0.5625 + -1.5z + z2 = 1.25 + 0.5625

Combine like terms: 1.25 + 0.5625 = 1.8125
0.5625 + -1.5z + z2 = 1.8125

Factor a perfect square on the left side:
(z + -0.75)(z + -0.75) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(z + -0.75) equal to 1.346291202 and -1.346291202.

Subproblem 1

z + -0.75 = 1.346291202 Simplifying z + -0.75 = 1.346291202 Reorder the terms: -0.75 + z = 1.346291202 Solving -0.75 + z = 1.346291202 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 = 1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + z = 1.346291202 + 0.75 z = 1.346291202 + 0.75 Combine like terms: 1.346291202 + 0.75 = 2.096291202 z = 2.096291202 Simplifying z = 2.096291202

Subproblem 2

z + -0.75 = -1.346291202 Simplifying z + -0.75 = -1.346291202 Reorder the terms: -0.75 + z = -1.346291202 Solving -0.75 + z = -1.346291202 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 = -1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + z = -1.346291202 + 0.75 z = -1.346291202 + 0.75 Combine like terms: -1.346291202 + 0.75 = -0.596291202 z = -0.596291202 Simplifying z = -0.596291202

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.096291202, -0.596291202}

See similar equations:

| 14c-2c=45 | | R^2-9r+18=0 | | 11x-x=90 | | N^2+9n+14=0 | | R^2-r-2=0 | | V^2-5v+6=0 | | P^2+3p-40=0 | | 53-3x=15x+21 | | 8-10x=53-45x | | 5x+4=5x-7 | | 13-8x=73-22x | | 4(5x+2)=19x-4 | | x^2-24x=0 | | 7x+13=2-7x | | 38-4x=5x+21 | | 6b+5b=-66 | | x^2+3x-156=0 | | a^2-18a+80=0 | | 3x+x-3=13 | | 0x-3=3 | | 10=-16t^2+50t+4 | | 8(2x+5)(2x-5)=0 | | 16+n=8 | | -5y+2=-9y-6 | | 3.75x+55=2.50x+75 | | (4v-7)(6v+8)v= | | 0=-16t^2+8t+80 | | -5(3y+2)=5 | | 3(2-x)+x=2(3-x) | | (r-4)(r-4)=0 | | -7(4b+3)+(29b-8)=0 | | (28b-4)-9(3b+4)=-2 |

Equations solver categories