y^2+14y+52=78

Simple and best practice solution for y^2+14y+52=78 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 y^2+14y+52=78 equation: 


Simplifying
y2 + 14y + 52 = 78

Reorder the terms:
52 + 14y + y2 = 78

Solving
52 + 14y + y2 = 78

Solving for variable 'y'.

Reorder the terms:
52 + -78 + 14y + y2 = 78 + -78

Combine like terms: 52 + -78 = -26
-26 + 14y + y2 = 78 + -78

Combine like terms: 78 + -78 = 0
-26 + 14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 14y + 26 + y2 = 0 + 26

Reorder the terms:
-26 + 26 + 14y + y2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 14y + y2 = 0 + 26
14y + y2 = 0 + 26

Combine like terms: 0 + 26 = 26
14y + y2 = 26

The y term is 14y.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14y + 49 + y2 = 26 + 49

Reorder the terms:
49 + 14y + y2 = 26 + 49

Combine like terms: 26 + 49 = 75
49 + 14y + y2 = 75

Factor a perfect square on the left side:
(y + 7)(y + 7) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(y + 7) equal to 8.660254038 and -8.660254038.


Subproblem 1
y + 7 = 8.660254038

Simplifying
y + 7 = 8.660254038

Reorder the terms:
7 + y = 8.660254038

Solving
7 + y = 8.660254038

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = 8.660254038 + -7

Combine like terms: 7 + -7 = 0
0 + y = 8.660254038 + -7
y = 8.660254038 + -7

Combine like terms: 8.660254038 + -7 = 1.660254038
y = 1.660254038

Simplifying
y = 1.660254038


Subproblem 2
y + 7 = -8.660254038

Simplifying
y + 7 = -8.660254038

Reorder the terms:
7 + y = -8.660254038

Solving
7 + y = -8.660254038

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = -8.660254038 + -7

Combine like terms: 7 + -7 = 0
0 + y = -8.660254038 + -7
y = -8.660254038 + -7

Combine like terms: -8.660254038 + -7 = -15.660254038
y = -15.660254038

Simplifying
y = -15.660254038


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.660254038, -15.660254038}

See similar equations:

| x-4=-2x^2-x | | ax+b=9 | | 4x-2=-3x+x-2 | | -2+12x=10+10x | | 4+7q=6+6q | | 7x-4+2x=23 | | -x+1+10x=-3+5x+24 | | -2+2x=10+10x | | (4y+8)(y+2)=0 | | (4x-1)(7x+6)=0 | | x+5x+6x=72 | | 7x+8y=892 | | -x+2+11x=-4+4x+24 | | 2(5-11)+15=3(g-7)-7 | | 4(5+a)=0 | | 2(x-3)+3y=5y-2(3-5x)fory | | (x)=[[x]]-2 | | F(x)=[[x]]-2 | | 3d+8=d+20 | | z=x+(z-x) | | 1.98=x^2+x | | lg(3x+20)=2 | | 4w+3=20-6a | | 8(-4+y)= | | 9r-5=85 | | 101+c= | | 17(2)-16= | | 2p-3=-19 | | -(-11+b)=16 | | 256(5)+3(11)= | | 5x-7=8x-58 | | 6+4=4 |

Equations solver categories