-y^2=4y-23

Simple and best practice solution for -y^2=4y-23 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=4y-23 equation:


Simplifying
-1y2 = 4y + -23

Reorder the terms:
-1y2 = -23 + 4y

Solving
-1y2 = -23 + 4y

Solving for variable 'y'.

Reorder the terms:
23 + -4y + -1y2 = -23 + 4y + 23 + -4y

Reorder the terms:
23 + -4y + -1y2 = -23 + 23 + 4y + -4y

Combine like terms: -23 + 23 = 0
23 + -4y + -1y2 = 0 + 4y + -4y
23 + -4y + -1y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
23 + -4y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-23 + 4y + y2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 4y + 23 + y2 = 0 + 23

Reorder the terms:
-23 + 23 + 4y + y2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 4y + y2 = 0 + 23
4y + y2 = 0 + 23

Combine like terms: 0 + 23 = 23
4y + y2 = 23

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 23 + 4

Reorder the terms:
4 + 4y + y2 = 23 + 4

Combine like terms: 23 + 4 = 27
4 + 4y + y2 = 27

Factor a perfect square on the left side:
(y + 2)(y + 2) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(y + 2) equal to 5.196152423 and -5.196152423.

Subproblem 1

y + 2 = 5.196152423 Simplifying y + 2 = 5.196152423 Reorder the terms: 2 + y = 5.196152423 Solving 2 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + y = 5.196152423 + -2 y = 5.196152423 + -2 Combine like terms: 5.196152423 + -2 = 3.196152423 y = 3.196152423 Simplifying y = 3.196152423

Subproblem 2

y + 2 = -5.196152423 Simplifying y + 2 = -5.196152423 Reorder the terms: 2 + y = -5.196152423 Solving 2 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -5.196152423 + -2 Combine like terms: 2 + -2 = 0 0 + y = -5.196152423 + -2 y = -5.196152423 + -2 Combine like terms: -5.196152423 + -2 = -7.196152423 y = -7.196152423 Simplifying y = -7.196152423

Solution

The solution to the problem is based on the solutions from the subproblems. y = {3.196152423, -7.196152423}

See similar equations:

| y^2=-2y+8 | | 10u+-2u= | | 4t^2-5t=0 | | 2x*2+-8x*2= | | 5c+25=85 | | 2y^3-9y^2-5y=0 | | 4ab-3a=0 | | 2a*2b*3+2a*3b*2-6a*3b*3+2a*2= | | 4ab+b=5 | | -2y*2+9y*2= | | x^2-4x+8= | | W-8+34=26+8 | | 4ln(6x)=12 | | 12x-x(-4x)= | | -7xy-9-(-4xy)= | | 122-2x=34x+22 | | -2y^2-11y=-6 | | 6(2x-3)-(5x+2)=-2(4x+1) | | 12uv-(-6w)-7uv= | | X^3-10x^2+10=0 | | 6-9x=18-16x | | 8ef+2a-5ef= | | y=3(3)-4 | | -12abc+2abc-8= | | y=-x^2-18x+90 | | -2xy+2-4xy-(-13)= | | -136-10x=7x+17 | | 7ab-6ab= | | 0.5y+4=2 | | -x^2+11x+12=0 | | 5-7x=32-28x | | 10f+6e+3e-12f= |

Equations solver categories