7y^2-16y-24=0

Simple and best practice solution for 7y^2-16y-24=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 7y^2-16y-24=0 equation:


Simplifying
7y2 + -16y + -24 = 0

Reorder the terms:
-24 + -16y + 7y2 = 0

Solving
-24 + -16y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
-3.428571429 + -2.285714286y + y2 = 0

Move the constant term to the right:

Add '3.428571429' to each side of the equation.
-3.428571429 + -2.285714286y + 3.428571429 + y2 = 0 + 3.428571429

Reorder the terms:
-3.428571429 + 3.428571429 + -2.285714286y + y2 = 0 + 3.428571429

Combine like terms: -3.428571429 + 3.428571429 = 0.000000000
0.000000000 + -2.285714286y + y2 = 0 + 3.428571429
-2.285714286y + y2 = 0 + 3.428571429

Combine like terms: 0 + 3.428571429 = 3.428571429
-2.285714286y + y2 = 3.428571429

The y term is -2.285714286y.  Take half its coefficient (-1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
-2.285714286y + 1.306122449 + y2 = 3.428571429 + 1.306122449

Reorder the terms:
1.306122449 + -2.285714286y + y2 = 3.428571429 + 1.306122449

Combine like terms: 3.428571429 + 1.306122449 = 4.734693878
1.306122449 + -2.285714286y + y2 = 4.734693878

Factor a perfect square on the left side:
(y + -1.142857143)(y + -1.142857143) = 4.734693878

Calculate the square root of the right side: 2.175935173

Break this problem into two subproblems by setting 
(y + -1.142857143) equal to 2.175935173 and -2.175935173.

Subproblem 1

y + -1.142857143 = 2.175935173 Simplifying y + -1.142857143 = 2.175935173 Reorder the terms: -1.142857143 + y = 2.175935173 Solving -1.142857143 + y = 2.175935173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + y = 2.175935173 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = 2.175935173 + 1.142857143 y = 2.175935173 + 1.142857143 Combine like terms: 2.175935173 + 1.142857143 = 3.318792316 y = 3.318792316 Simplifying y = 3.318792316

Subproblem 2

y + -1.142857143 = -2.175935173 Simplifying y + -1.142857143 = -2.175935173 Reorder the terms: -1.142857143 + y = -2.175935173 Solving -1.142857143 + y = -2.175935173 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.142857143' to each side of the equation. -1.142857143 + 1.142857143 + y = -2.175935173 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + y = -2.175935173 + 1.142857143 y = -2.175935173 + 1.142857143 Combine like terms: -2.175935173 + 1.142857143 = -1.03307803 y = -1.03307803 Simplifying y = -1.03307803

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.318792316, -1.03307803}

See similar equations:

| 6p+6=-8-4p | | -3x/-4=3 | | 26/5x=-91/35 | | (3y-2)+(7y+8)= | | 4x-6x=16-6x | | x^2-12.26x=336 | | Y=4x^2+30x+900 | | 6(x-3)+2x=39 | | 5/3×3/10 | | 112/3x=25 | | 25/5x=-21/35 | | 3x(x+6)=26 | | 22x+6x= | | -6+5c=15+c | | X=10X-3 | | 4z-5=29 | | 7e+2=3e-8 | | 3m-(1-m)=2m | | 7-3y-1=-2y | | 14x=91 | | 3m-(-m)=2m | | s=2t^2-t+5 | | 5/500 | | x*0.01=5 | | 3y-5+y=-2y+7 | | 6x^2-44=0 | | 1/y=10000-x | | X^4=5.7 | | 9x+21x=14x | | x^2-100000x+3000000=0 | | 0-6n(4n-1)= | | 4s-29=87 |

Equations solver categories