16y^2-14y-7=0

Simple and best practice solution for 16y^2-14y-7=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 16y^2-14y-7=0 equation:


Simplifying
16y2 + -14y + -7 = 0

Reorder the terms:
-7 + -14y + 16y2 = 0

Solving
-7 + -14y + 16y2 = 0

Solving for variable 'y'.

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

Divide each side by '16'.
-0.4375 + -0.875y + y2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -0.875y + 0.4375 + y2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -0.875y + y2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -0.875y + y2 = 0 + 0.4375
-0.875y + y2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-0.875y + y2 = 0.4375

The y term is -0.875y.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875y + 0.19140625 + y2 = 0.4375 + 0.19140625

Reorder the terms:
0.19140625 + -0.875y + y2 = 0.4375 + 0.19140625

Combine like terms: 0.4375 + 0.19140625 = 0.62890625
0.19140625 + -0.875y + y2 = 0.62890625

Factor a perfect square on the left side:
(y + -0.4375)(y + -0.4375) = 0.62890625

Calculate the square root of the right side: 0.793036096

Break this problem into two subproblems by setting 
(y + -0.4375) equal to 0.793036096 and -0.793036096.

Subproblem 1

y + -0.4375 = 0.793036096 Simplifying y + -0.4375 = 0.793036096 Reorder the terms: -0.4375 + y = 0.793036096 Solving -0.4375 + y = 0.793036096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = 0.793036096 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = 0.793036096 + 0.4375 y = 0.793036096 + 0.4375 Combine like terms: 0.793036096 + 0.4375 = 1.230536096 y = 1.230536096 Simplifying y = 1.230536096

Subproblem 2

y + -0.4375 = -0.793036096 Simplifying y + -0.4375 = -0.793036096 Reorder the terms: -0.4375 + y = -0.793036096 Solving -0.4375 + y = -0.793036096 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + y = -0.793036096 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + y = -0.793036096 + 0.4375 y = -0.793036096 + 0.4375 Combine like terms: -0.793036096 + 0.4375 = -0.355536096 y = -0.355536096 Simplifying y = -0.355536096

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.230536096, -0.355536096}

See similar equations:

| (z-2)5+2=7 | | -(8x-7)= | | 2k=90-8k | | (y-8)-(y+7)=4y | | y=57-2y | | 16m=45+11m | | 8x-(9x+9)=5x-22 | | x^2+25x=10 | | x^2+25x=10x | | 2x+7=x-3 | | 25v^2=1 | | x+x*x-x=30 | | x^2+35x=0 | | 7x+25=3x-11 | | -4x^2-5+x^4=0 | | 7x+7=3x-11 | | 14x^2-57x+28=0 | | 4x+352= | | -7-13=6x+15-5x | | m-6=1/2(8-18m) | | x-x^2-12=2x+x+48 | | -7+12=m-6 | | 1/3(12-9n)=4-3n | | 8v+77=5(5-v) | | 3(f+7)=2f | | -8(t+1)=8 | | -1.2x+3.0=-0.6 | | 5c+1=-1+5c | | 2z=1.9+.3 | | 59+x=2-2x | | 3-d=7d+27 | | 2(3x-3)=7x |

Equations solver categories