y^2-10y=-22

Simple and best practice solution for y^2-10y=-22 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^2-10y=-22 equation:


Simplifying
y2 + -10y = -22

Reorder the terms:
-10y + y2 = -22

Solving
-10y + y2 = -22

Solving for variable 'y'.

Reorder the terms:
22 + -10y + y2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -10y + -22 + y2 = 0 + -22

Reorder the terms:
22 + -22 + -10y + y2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -10y + y2 = 0 + -22
-10y + y2 = 0 + -22

Combine like terms: 0 + -22 = -22
-10y + y2 = -22

The y term is -10y.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10y + 25 + y2 = -22 + 25

Reorder the terms:
25 + -10y + y2 = -22 + 25

Combine like terms: -22 + 25 = 3
25 + -10y + y2 = 3

Factor a perfect square on the left side:
(y + -5)(y + -5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + -5) equal to 1.732050808 and -1.732050808.

Subproblem 1

y + -5 = 1.732050808 Simplifying y + -5 = 1.732050808 Reorder the terms: -5 + y = 1.732050808 Solving -5 + y = 1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + y = 1.732050808 + 5 y = 1.732050808 + 5 Combine like terms: 1.732050808 + 5 = 6.732050808 y = 6.732050808 Simplifying y = 6.732050808

Subproblem 2

y + -5 = -1.732050808 Simplifying y + -5 = -1.732050808 Reorder the terms: -5 + y = -1.732050808 Solving -5 + y = -1.732050808 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + y = -1.732050808 + 5 y = -1.732050808 + 5 Combine like terms: -1.732050808 + 5 = 3.267949192 y = 3.267949192 Simplifying y = 3.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. y = {6.732050808, 3.267949192}

See similar equations:

| -(4y+4)-(-3y-5)=-6 | | r^2+3r-3=0 | | -3a-0.50=1 | | 5x-3y=1 | | 8(x+7)-3=53 | | 16x^2-48x+36=49 | | y=0.1x+210 | | g^2-8g+16=2 | | y=x^3+8x^2-21x+2 | | 3-(3x-1)=2(x+3)-1 | | m-8.3=-6.8 | | 0.08(12)+0.02x=0.04(12+x) | | x+5(4)=56 | | 3x^8-7x^8= | | m+26=19 | | m-26=19 | | 5(x+4)+12=2(x-3)-1 | | x+5*4=56 | | 8-t^2=0 | | -5(x+3)+7x=-7 | | 0.36(24)+0.04=0.12(24+x) | | 10n+8=88 | | 3n+5=17 | | 5-(x+3)+7x=-7 | | 0.20(24)+0.05=0.10(12+x) | | 4(3y-1)-3(2y)=6 | | -(6y+5)-(-5y-6)=-5 | | 5p-7=8 | | .135=.05*x | | -24+x=x+17 | | 5(x*4)+12=2(x-3)-1 | | -25+w=w+17 |

Equations solver categories