(4y^2)-19y-60=0

Simple and best practice solution for (4y^2)-19y-60=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 (4y^2)-19y-60=0 equation:


Simplifying
(4y2) + -19y + -60 = 0

Reorder the terms:
-60 + -19y + (4y2) = 0

Solving
-60 + -19y + (4y2) = 0

Solving for variable 'y'.

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

Divide each side by '4'.
-15 + -4.75y + y2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -4.75y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + -4.75y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4.75y + y2 = 0 + 15
-4.75y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
-4.75y + y2 = 15

The y term is -4.75y.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75y + 5.640625 + y2 = 15 + 5.640625

Reorder the terms:
5.640625 + -4.75y + y2 = 15 + 5.640625

Combine like terms: 15 + 5.640625 = 20.640625
5.640625 + -4.75y + y2 = 20.640625

Factor a perfect square on the left side:
((y) + -2.375)((y) + -2.375) = 20.640625

Calculate the square root of the right side: 4.543195461

Break this problem into two subproblems by setting 
((y) + -2.375) equal to 4.543195461 and -4.543195461.

Subproblem 1

(y) + -2.375 = 4.543195461 Simplifying (y) + -2.375 = 4.543195461 y + -2.375 = 4.543195461 Reorder the terms: -2.375 + y = 4.543195461 Solving -2.375 + y = 4.543195461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + y = 4.543195461 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + y = 4.543195461 + 2.375 y = 4.543195461 + 2.375 Combine like terms: 4.543195461 + 2.375 = 6.918195461 y = 6.918195461 Simplifying y = 6.918195461

Subproblem 2

(y) + -2.375 = -4.543195461 Simplifying (y) + -2.375 = -4.543195461 y + -2.375 = -4.543195461 Reorder the terms: -2.375 + y = -4.543195461 Solving -2.375 + y = -4.543195461 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + y = -4.543195461 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + y = -4.543195461 + 2.375 y = -4.543195461 + 2.375 Combine like terms: -4.543195461 + 2.375 = -2.168195461 y = -2.168195461 Simplifying y = -2.168195461

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.918195461, -2.168195461}

See similar equations:

| 14x=-9x | | 275c+125w=86000 | | 8x-z=yforx | | 100x^2=15x | | =1000(1+125) | | 3x^2y+5yx^2-6xy^2= | | 100x^2=100x | | 11x+4(2-x)=7x+10 | | y=3.8x-5.5 | | 2y+16=64 | | 2c+4d=102 | | 5/4(12y) | | =-x^2-4x+3 | | (f)x=-x^2-4x+3 | | x+.014x=18590 | | C=zw+zforw | | 2x-6=183-y | | 2x-6=183-9 | | 7c-8-2c=18 | | 49+y^2+10y=8x | | 90=10o-90 | | 19=(-5)x-6(-3x+15)+5 | | 4x-21+3x+77=180 | | 9m-16=10m+13 | | 50=32-2(-4-2w) | | 9x+7y=-5 | | (10x+5)=6 | | (1)+(1)+(1)+(3)+(1)+(-5)+(-2)+(1)+(2)+(1)= | | 2x+6-2=5x-1 | | -6x-3=-4 | | 4x+7=6-3(x+1) | | 4(3a-5)=28 |

Equations solver categories