x^2-x-5=0

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


Simplifying
x2 + -1x + -5 = 0

Reorder the terms:
-5 + -1x + x2 = 0

Solving
-5 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -1x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x + x2 = 0 + 5
-1x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1x + x2 = 5

The x term is -1x.  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.
-1x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -1x + x2 = 5.25

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

Calculate the square root of the right side: 2.291287847

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

Subproblem 1

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

Subproblem 2

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

Solution

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

See similar equations:

| 2b+4a+3b= | | 16st-3st= | | 5.4s+2.8s= | | x(x-4)-20=0 | | 2ax+7ax= | | x(x-4)=20 | | 2v-5x+3v+w= | | 2x^2+14x+12=0 | | 5-4x-3=4 | | 490=114x-227524 | | 112-44x+4x^2=0 | | -35+7y+7=3(3y-2)-6 | | 12x^2-7x+1=0 | | x^3+7x^2-78=0 | | i=114x-227524 | | 3x^4+27x^2+18x^3=0 | | -4(4p+4)-46=5(5p+4) | | 6x^3-24x=0 | | 9. 6x^3-24x=0 | | 23x=-529 | | 5v+4=5v+4 | | 10x-2=34 | | 8x-7=19x+5 | | 3x^3+11x^2+6x=0 | | 7x-8=-64 | | 2m+5= | | 4rs^4+3r^2s+4r-4rs^4+5+9s= | | 0=-2(y+8) | | 10s-14s=16 | | -10s-14s=16 | | 15x-20y=1 | | 0.43+2x=-17.6 |

Equations solver categories