v^2-v-5=0

Simple and best practice solution for v^2-v-5=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 v^2-v-5=0 equation:


Simplifying
v2 + -1v + -5 = 0

Reorder the terms:
-5 + -1v + v2 = 0

Solving
-5 + -1v + v2 = 0

Solving for variable 'v'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1v + 5 + v2 = 0 + 5

Reorder the terms:
-5 + 5 + -1v + v2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1v + v2 = 0 + 5
-1v + v2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1v + v2 = 5

The v term is -1v.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1v + 0.25 + v2 = 5 + 0.25

Reorder the terms:
0.25 + -1v + v2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -1v + v2 = 5.25

Factor a perfect square on the left side:
(v + -0.5)(v + -0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(v + -0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

v + -0.5 = 2.291287847 Simplifying v + -0.5 = 2.291287847 Reorder the terms: -0.5 + v = 2.291287847 Solving -0.5 + v = 2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = 2.291287847 + 0.5 v = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 v = 2.791287847 Simplifying v = 2.791287847

Subproblem 2

v + -0.5 = -2.291287847 Simplifying v + -0.5 = -2.291287847 Reorder the terms: -0.5 + v = -2.291287847 Solving -0.5 + v = -2.291287847 Solving for variable 'v'. Move all terms containing v to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + v = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + v = -2.291287847 + 0.5 v = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 v = -1.791287847 Simplifying v = -1.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. v = {2.791287847, -1.791287847}

See similar equations:

| -38-(-19)= | | -10=5(y+7) | | -31+(-38)-(-19)-14= | | 2(x+5)=x-18 | | -8+4=6x+12 | | 18-h=13 | | 9t^2+72t=0 | | 5y-6+y+28=6y+30-4y | | -7x+3(4x+10)=80 | | 10n+8=74 | | 5-6n+2n=7-98 | | -4(3p+4)-42=2(5p+4) | | (x-5/x-6)=(7/6-x) | | .07x+.04y=15 | | -5y-9=16 | | -23+8y+7=2(5y-2)-2 | | 18+2y-1=11y-11-5y | | -3n=10-2n | | y=-0.1(34)+12 | | 3x+20=2(x+20) | | 1/3(x-4)=7x-10 | | 10b-3=-78 | | 8x-4-x=-5 | | (Y+7)(Y-5)=0 | | 16+9d=-14 | | 2x/25•5x/16x | | 35=-2x+56 | | 7/2m | | 1b+1b-10=22 | | 3y-(y-6)=-2 | | (X+2)(-6x^2+2x-4)= | | 3/18-2k=13 |

Equations solver categories