y^2+18y+53=0

Simple and best practice solution for y^2+18y+53=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 y^2+18y+53=0 equation:


Simplifying
y2 + 18y + 53 = 0

Reorder the terms:
53 + 18y + y2 = 0

Solving
53 + 18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-53' to each side of the equation.
53 + 18y + -53 + y2 = 0 + -53

Reorder the terms:
53 + -53 + 18y + y2 = 0 + -53

Combine like terms: 53 + -53 = 0
0 + 18y + y2 = 0 + -53
18y + y2 = 0 + -53

Combine like terms: 0 + -53 = -53
18y + y2 = -53

The y term is 18y.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18y + 81 + y2 = -53 + 81

Reorder the terms:
81 + 18y + y2 = -53 + 81

Combine like terms: -53 + 81 = 28
81 + 18y + y2 = 28

Factor a perfect square on the left side:
(y + 9)(y + 9) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(y + 9) equal to 5.291502622 and -5.291502622.

Subproblem 1

y + 9 = 5.291502622 Simplifying y + 9 = 5.291502622 Reorder the terms: 9 + y = 5.291502622 Solving 9 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + y = 5.291502622 + -9 y = 5.291502622 + -9 Combine like terms: 5.291502622 + -9 = -3.708497378 y = -3.708497378 Simplifying y = -3.708497378

Subproblem 2

y + 9 = -5.291502622 Simplifying y + 9 = -5.291502622 Reorder the terms: 9 + y = -5.291502622 Solving 9 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = -5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + y = -5.291502622 + -9 y = -5.291502622 + -9 Combine like terms: -5.291502622 + -9 = -14.291502622 y = -14.291502622 Simplifying y = -14.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-3.708497378, -14.291502622}

See similar equations:

| x+76=18 | | R(x)=-25x^2+100x+1500 | | 16x-8x+12=78+28 | | 21=10x-89 | | 6y+8=5y-6 | | 18-6y=4y-4(y+3) | | 10x-2=60 | | 12x+7=52 | | p(x)=3x^3+6x^2-9x | | 83=6x+11 | | X^5x+4=0 | | 20=p+16 | | 5-x^2=0equation | | 6x+35+9x=15[x+4]-25 | | -0.25(x-12)0.5(x+2)=x+4 | | n+2__25=n-4__35 | | 133-2x=25x+22 | | 3(a+2)-(a-1)=17 | | 45x=3 | | 24x-2=24x-7 | | 5/9+w=7/9 | | 5x-2-3x[1+2]=2[2+3] | | 8-9=w-2_6 | | f=2(g)(h) | | 5-x^2=0 | | 9+n=-4 | | x+1.2=3.5 | | (2y-5)(7-y)=0 | | x^3=7x^2 | | 33=9+11+c | | 5(7-x)+12x=0 | | 6x-5=7x+15 |

Equations solver categories