8y^2-23y-15=0

Simple and best practice solution for 8y^2-23y-15=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 8y^2-23y-15=0 equation:


Simplifying
8y2 + -23y + -15 = 0

Reorder the terms:
-15 + -23y + 8y2 = 0

Solving
-15 + -23y + 8y2 = 0

Solving for variable 'y'.

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

Divide each side by '8'.
-1.875 + -2.875y + y2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -2.875y + 1.875 + y2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -2.875y + y2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -2.875y + y2 = 0 + 1.875
-2.875y + y2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-2.875y + y2 = 1.875

The y term is -2.875y.  Take half its coefficient (-1.4375).
Square it (2.06640625) and add it to both sides.

Add '2.06640625' to each side of the equation.
-2.875y + 2.06640625 + y2 = 1.875 + 2.06640625

Reorder the terms:
2.06640625 + -2.875y + y2 = 1.875 + 2.06640625

Combine like terms: 1.875 + 2.06640625 = 3.94140625
2.06640625 + -2.875y + y2 = 3.94140625

Factor a perfect square on the left side:
(y + -1.4375)(y + -1.4375) = 3.94140625

Calculate the square root of the right side: 1.985297522

Break this problem into two subproblems by setting 
(y + -1.4375) equal to 1.985297522 and -1.985297522.

Subproblem 1

y + -1.4375 = 1.985297522 Simplifying y + -1.4375 = 1.985297522 Reorder the terms: -1.4375 + y = 1.985297522 Solving -1.4375 + y = 1.985297522 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + y = 1.985297522 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + y = 1.985297522 + 1.4375 y = 1.985297522 + 1.4375 Combine like terms: 1.985297522 + 1.4375 = 3.422797522 y = 3.422797522 Simplifying y = 3.422797522

Subproblem 2

y + -1.4375 = -1.985297522 Simplifying y + -1.4375 = -1.985297522 Reorder the terms: -1.4375 + y = -1.985297522 Solving -1.4375 + y = -1.985297522 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + y = -1.985297522 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + y = -1.985297522 + 1.4375 y = -1.985297522 + 1.4375 Combine like terms: -1.985297522 + 1.4375 = -0.547797522 y = -0.547797522 Simplifying y = -0.547797522

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.422797522, -0.547797522}

See similar equations:

| b^2+2b=35 | | 2x+4-34=5x-6 | | 24x^2+4=24x | | 3(y^2-6)=y(y+7)-3 | | 20Y+4=48 | | 3x^2+7xy+3y^2=1 | | 7x+18=95 | | x^3+4x^2-15x-72=0 | | 6m+4n-3m+10n= | | 33(3x+5x)=115 | | -10+5x-3x=-8 | | -38=x+6x+4 | | 4+11x=4+x | | b(2b+3)-2b(b-5)=6 | | 2x+3+x=39 | | 7+55x=44x+10 | | F=G+Grt | | 5x+8=-55-4x | | 7n+14= | | x+((x*0.23)-(x*0.20))=721 | | x+((x*0.20)-(x*0.20))=721 | | 8(-6-h)=16 | | y=10sinx | | 2(4x-10)=7x-10 | | 8x-7x=10+20 | | 50y-4-80y-12-10y+1=0 | | 9t+10=73 | | 1.25j=j+3 | | 3(x-1)-2(x+2)=-2 | | 52x-45-81x+33x=3x-5 | | b(b+2)=35 | | 3(x-1)-3(x+2)=-2 |

Equations solver categories