y^2-6y-13=0

Simple and best practice solution for y^2-6y-13=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^2-6y-13=0 equation:


Simplifying
y2 + -6y + -13 = 0

Reorder the terms:
-13 + -6y + y2 = 0

Solving
-13 + -6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -6y + 13 + y2 = 0 + 13

Reorder the terms:
-13 + 13 + -6y + y2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6y + y2 = 0 + 13
-6y + y2 = 0 + 13

Combine like terms: 0 + 13 = 13
-6y + y2 = 13

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = 13 + 9

Reorder the terms:
9 + -6y + y2 = 13 + 9

Combine like terms: 13 + 9 = 22
9 + -6y + y2 = 22

Factor a perfect square on the left side:
(y + -3)(y + -3) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + -3) equal to 4.69041576 and -4.69041576.

Subproblem 1

y + -3 = 4.69041576 Simplifying y + -3 = 4.69041576 Reorder the terms: -3 + y = 4.69041576 Solving -3 + y = 4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.69041576 + 3 y = 4.69041576 + 3 Combine like terms: 4.69041576 + 3 = 7.69041576 y = 7.69041576 Simplifying y = 7.69041576

Subproblem 2

y + -3 = -4.69041576 Simplifying y + -3 = -4.69041576 Reorder the terms: -3 + y = -4.69041576 Solving -3 + y = -4.69041576 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -4.69041576 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.69041576 + 3 y = -4.69041576 + 3 Combine like terms: -4.69041576 + 3 = -1.69041576 y = -1.69041576 Simplifying y = -1.69041576

Solution

The solution to the problem is based on the solutions from the subproblems. y = {7.69041576, -1.69041576}

See similar equations:

| 6x^2-16x=180-22x | | (-6)+8-10= | | Vxy-xz+3y-3z= | | 12t=t^2 | | 6+v+2=11 | | (m-1)x^2+3mx-5m+c=2 | | 18-4x=(-2) | | 4x^3+23x^2+15x= | | -19=3(n+2)-(1-3n) | | 2m+12-3m=-31 | | 5x^2+20x=160 | | -6(-2+2n)=-4(6n-6) | | (m-1)x^2+3mx-5m+c=0 | | 480+24(h-40)=840 | | 3x+4-3=x-3 | | 5(7n+4)=5(-6n+4) | | 11=10(k-9) | | -15x+3(2x-5)=-19-8x | | 4xy-8y= | | B^2-bx+b=4 | | x^3+2*x^2-4x-8=0 | | 30=-8(b-4)+6(2b-3) | | -25+n=-5(1-n) | | 8+10y=9y-10 | | -15x+3(2x-5)=19-8x | | 6(3x+7)=26+2x | | -2x^2-12x+5-x+8x^2+n= | | -4+4y-4y=-4 | | 2xsquared=200 | | 3(x-4)+6x-3=x | | 5x+5=7x-7 | | -5=6-(8-a) |

Equations solver categories