4y^2+7y-27=0

Simple and best practice solution for 4y^2+7y-27=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+7y-27=0 equation: 


Simplifying
4y2 + 7y + -27 = 0

Reorder the terms:
-27 + 7y + 4y2 = 0

Solving
-27 + 7y + 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'.
-6.75 + 1.75y + y2 = 0

Move the constant term to the right:

Add '6.75' to each side of the equation.
-6.75 + 1.75y + 6.75 + y2 = 0 + 6.75

Reorder the terms:
-6.75 + 6.75 + 1.75y + y2 = 0 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + 1.75y + y2 = 0 + 6.75
1.75y + y2 = 0 + 6.75

Combine like terms: 0 + 6.75 = 6.75
1.75y + y2 = 6.75

The y term is 1.75y.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75y + 0.765625 + y2 = 6.75 + 0.765625

Reorder the terms:
0.765625 + 1.75y + y2 = 6.75 + 0.765625

Combine like terms: 6.75 + 0.765625 = 7.515625
0.765625 + 1.75y + y2 = 7.515625

Factor a perfect square on the left side:
(y + 0.875)(y + 0.875) = 7.515625

Calculate the square root of the right side: 2.741464025

Break this problem into two subproblems by setting 
(y + 0.875) equal to 2.741464025 and -2.741464025.


Subproblem 1
y + 0.875 = 2.741464025

Simplifying
y + 0.875 = 2.741464025

Reorder the terms:
0.875 + y = 2.741464025

Solving
0.875 + y = 2.741464025

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + y = 2.741464025 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + y = 2.741464025 + -0.875
y = 2.741464025 + -0.875

Combine like terms: 2.741464025 + -0.875 = 1.866464025
y = 1.866464025

Simplifying
y = 1.866464025


Subproblem 2
y + 0.875 = -2.741464025

Simplifying
y + 0.875 = -2.741464025

Reorder the terms:
0.875 + y = -2.741464025

Solving
0.875 + y = -2.741464025

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-0.875' to each side of the equation.
0.875 + -0.875 + y = -2.741464025 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + y = -2.741464025 + -0.875
y = -2.741464025 + -0.875

Combine like terms: -2.741464025 + -0.875 = -3.616464025
y = -3.616464025

Simplifying
y = -3.616464025


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.866464025, -3.616464025}

See similar equations:

| x=6/2=x-5 | | Cos(55)=7/x | | -(3x+2)=-23 | | 3x^4-5x+3=0 | | 2x+6y=-48 | | 8x-39=2x+63 | | 68=17x | | 8a+3b+8a-4b= | | 3x+31=16x+17 | | a=15(2) | | 8(6c+m-5)= | | Y=7/(×-1)^2 | | 2x^3+17x^2+21x=0 | | 0.6=1-(18/x) | | 5m^2+2m+5=21 | | 32/4x(3-7)= | | (C-4)/5=7 | | Y=-.1X+27 | | y=1/2(-3)-1 | | 9x-7=3x+10 | | 1/2r-3=3(4-3/5r) | | 5.8m-18.6=1.87+12.2m-4.3m | | 3(x-4)=30-4x | | 2(x-1)=x+0 | | 4+5x=14+x | | 6x-2+46=180 | | y=-4-7 | | 2/×-4 | | 0.08x=7.50-0.05x | | 2y+62=6x | | 4x-5=10+x | | y-7=1/2x-4 |

Equations solver categories