2z^2+19z+20=0

Simple and best practice solution for 2z^2+19z+20=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 2z^2+19z+20=0 equation:


Simplifying
2z2 + 19z + 20 = 0

Reorder the terms:
20 + 19z + 2z2 = 0

Solving
20 + 19z + 2z2 = 0

Solving for variable 'z'.

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

Divide each side by '2'.
10 + 9.5z + z2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 9.5z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + 9.5z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 9.5z + z2 = 0 + -10
9.5z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
9.5z + z2 = -10

The z term is 9.5z.  Take half its coefficient (4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
9.5z + 22.5625 + z2 = -10 + 22.5625

Reorder the terms:
22.5625 + 9.5z + z2 = -10 + 22.5625

Combine like terms: -10 + 22.5625 = 12.5625
22.5625 + 9.5z + z2 = 12.5625

Factor a perfect square on the left side:
(z + 4.75)(z + 4.75) = 12.5625

Calculate the square root of the right side: 3.54436172

Break this problem into two subproblems by setting 
(z + 4.75) equal to 3.54436172 and -3.54436172.

Subproblem 1

z + 4.75 = 3.54436172 Simplifying z + 4.75 = 3.54436172 Reorder the terms: 4.75 + z = 3.54436172 Solving 4.75 + z = 3.54436172 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + z = 3.54436172 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + z = 3.54436172 + -4.75 z = 3.54436172 + -4.75 Combine like terms: 3.54436172 + -4.75 = -1.20563828 z = -1.20563828 Simplifying z = -1.20563828

Subproblem 2

z + 4.75 = -3.54436172 Simplifying z + 4.75 = -3.54436172 Reorder the terms: 4.75 + z = -3.54436172 Solving 4.75 + z = -3.54436172 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + z = -3.54436172 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + z = -3.54436172 + -4.75 z = -3.54436172 + -4.75 Combine like terms: -3.54436172 + -4.75 = -8.29436172 z = -8.29436172 Simplifying z = -8.29436172

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-1.20563828, -8.29436172}

See similar equations:

| 11(a-3)=-2-9 | | 3x-12+2x-3= | | (5w-8)(4+w)=0 | | 3/4y=-21 | | Y=2+x+3 | | 5*3x=42 | | 175-125+43425=45900-175 | | -4u/7=-16 | | y=5+2x-16 | | 123*1/4= | | 3m+20=4m+10 | | 32pt=gal | | 18-f/3=-7 | | 2+6x=0 | | lb=64oz | | (9y^4-6y^3-5y+7)+(18y^4-2y^3-7y+8)= | | (y-1)(y+9)= | | 98-m=44 | | -20=-5/9w | | y=-2x^2-7x-6 | | 4y+48=180 | | 37-x=12 | | y=5+x-16 | | -2/-2= | | 3(x+2/5)=x1/3 | | x/-9-8=-4 | | 3(x+2/5)=1/3 | | 4+25/5+3*4 | | 4x^2+7=2 | | 15-n=7 | | 196x^2-9=0 | | 2.50X=100 |

Equations solver categories