2y^2-9y-19=0

Simple and best practice solution for 2y^2-9y-19=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 2y^2-9y-19=0 equation:


Simplifying
2y2 + -9y + -19 = 0

Reorder the terms:
-19 + -9y + 2y2 = 0

Solving
-19 + -9y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-9.5 + -4.5y + y2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -4.5y + 9.5 + y2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -4.5y + y2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -4.5y + y2 = 0 + 9.5
-4.5y + y2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-4.5y + y2 = 9.5

The y term is -4.5y.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5y + 5.0625 + y2 = 9.5 + 5.0625

Reorder the terms:
5.0625 + -4.5y + y2 = 9.5 + 5.0625

Combine like terms: 9.5 + 5.0625 = 14.5625
5.0625 + -4.5y + y2 = 14.5625

Factor a perfect square on the left side:
(y + -2.25)(y + -2.25) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(y + -2.25) equal to 3.816084381 and -3.816084381.

Subproblem 1

y + -2.25 = 3.816084381 Simplifying y + -2.25 = 3.816084381 Reorder the terms: -2.25 + y = 3.816084381 Solving -2.25 + y = 3.816084381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 3.816084381 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 3.816084381 + 2.25 y = 3.816084381 + 2.25 Combine like terms: 3.816084381 + 2.25 = 6.066084381 y = 6.066084381 Simplifying y = 6.066084381

Subproblem 2

y + -2.25 = -3.816084381 Simplifying y + -2.25 = -3.816084381 Reorder the terms: -2.25 + y = -3.816084381 Solving -2.25 + y = -3.816084381 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -3.816084381 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -3.816084381 + 2.25 y = -3.816084381 + 2.25 Combine like terms: -3.816084381 + 2.25 = -1.566084381 y = -1.566084381 Simplifying y = -1.566084381

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.066084381, -1.566084381}

See similar equations:

| (5a+3)=(15-a) | | 12-6x=8-7x | | 5x+5x+8x=30 | | v-.714=.666 | | 3x+7=-23-2x | | 3(2x-1)-6x=10x-7 | | ln+lnt=2 | | 3x-17=16-(2x-8) | | -2y-5=3 | | -2u-7=3 | | 2v+9=7 | | x(4-x^2)=x+2 | | 8m^2+19m-15=0 | | (x^3+5xy-10y^2)-(2x+9xy-4y^2)= | | X^3+x^2+ax=0 | | X^3+3x^2+ax=0 | | x(4-x^2)=0 | | 8xy-xy= | | 6x-15=2x+6 | | 3(a+1)+(5-b)+(10-c)=36 | | X^2-x-702=0 | | 9h-26=26 | | x-(3x+3)=11 | | (10-c)+(5c+1)+(25-4c)=36 | | (7-x)(3x-4)=0 | | 9x-4y=11fory | | (7x^2-6x-1)+(2x^2-5x+7)-(x^2-3x-2)= | | -2(x+5)-3=2-3(x+1) | | 8m-24=40 | | -5(x-7)=30-(2x+1) | | -5(x-7)=30-(2x-1) | | 11+1x=5+3x |

Equations solver categories