27y^2+6y-25=0

Simple and best practice solution for 27y^2+6y-25=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 27y^2+6y-25=0 equation:


Simplifying
27y2 + 6y + -25 = 0

Reorder the terms:
-25 + 6y + 27y2 = 0

Solving
-25 + 6y + 27y2 = 0

Solving for variable 'y'.

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

Divide each side by '27'.
-0.9259259259 + 0.2222222222y + y2 = 0

Move the constant term to the right:

Add '0.9259259259' to each side of the equation.
-0.9259259259 + 0.2222222222y + 0.9259259259 + y2 = 0 + 0.9259259259

Reorder the terms:
-0.9259259259 + 0.9259259259 + 0.2222222222y + y2 = 0 + 0.9259259259

Combine like terms: -0.9259259259 + 0.9259259259 = 0.0000000000
0.0000000000 + 0.2222222222y + y2 = 0 + 0.9259259259
0.2222222222y + y2 = 0 + 0.9259259259

Combine like terms: 0 + 0.9259259259 = 0.9259259259
0.2222222222y + y2 = 0.9259259259

The y term is 0.2222222222y.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222y + 0.01234567901 + y2 = 0.9259259259 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222y + y2 = 0.9259259259 + 0.01234567901

Combine like terms: 0.9259259259 + 0.01234567901 = 0.93827160491
0.01234567901 + 0.2222222222y + y2 = 0.93827160491

Factor a perfect square on the left side:
(y + 0.1111111111)(y + 0.1111111111) = 0.93827160491

Calculate the square root of the right side: 0.96864421

Break this problem into two subproblems by setting 
(y + 0.1111111111) equal to 0.96864421 and -0.96864421.

Subproblem 1

y + 0.1111111111 = 0.96864421 Simplifying y + 0.1111111111 = 0.96864421 Reorder the terms: 0.1111111111 + y = 0.96864421 Solving 0.1111111111 + y = 0.96864421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + y = 0.96864421 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + y = 0.96864421 + -0.1111111111 y = 0.96864421 + -0.1111111111 Combine like terms: 0.96864421 + -0.1111111111 = 0.8575330989 y = 0.8575330989 Simplifying y = 0.8575330989

Subproblem 2

y + 0.1111111111 = -0.96864421 Simplifying y + 0.1111111111 = -0.96864421 Reorder the terms: 0.1111111111 + y = -0.96864421 Solving 0.1111111111 + y = -0.96864421 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + y = -0.96864421 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + y = -0.96864421 + -0.1111111111 y = -0.96864421 + -0.1111111111 Combine like terms: -0.96864421 + -0.1111111111 = -1.0797553211 y = -1.0797553211 Simplifying y = -1.0797553211

Solution

The solution to the problem is based on the solutions from the subproblems. y = {0.8575330989, -1.0797553211}

See similar equations:

| 12y-7y-5=94.30 | | -h-15h-8h-10h=-20 | | 820.15=47(x+2.45) | | -4x+13=6 | | F(x)=3x^3-7x^2+4x | | 2(x+6)=24whatisx | | 8y-6y-11=25.42 | | n^3=7.84 | | 10m+m-9m+m-2m=17 | | -4/92/3c | | -4x/5-5=3 | | 4tanx=2sec^2x | | c=5.62+69.99 | | -5/7x-5 | | 12a-2a-5a-5a+4=16 | | 12x^2+20x^2= | | 24y=-24+18y | | V+6=2 | | 18/6-2 | | -6v+-12v-18v+5v=-20 | | x+27+2x-9=180 | | 5(a+6)-1= | | 11-z=7 | | 5h+5h=20 | | 10k^2-97=3k^2+659 | | (3x-30)=100-(x/2) | | 128/8 | | 9a-2a-a=-11 | | 28+x=6+3x | | 34=3v-8 | | 2v^2-47=61 | | 9+145= |

Equations solver categories