5-x(x-1)=4

Simple and best practice solution for 5-x(x-1)=4 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 5-x(x-1)=4 equation:


Simplifying
5 + -1x(x + -1) = 4

Reorder the terms:
5 + -1x(-1 + x) = 4
5 + (-1 * -1x + x * -1x) = 4
5 + (1x + -1x2) = 4

Solving
5 + 1x + -1x2 = 4

Solving for variable 'x'.

Reorder the terms:
5 + -4 + 1x + -1x2 = 4 + -4

Combine like terms: 5 + -4 = 1
1 + 1x + -1x2 = 4 + -4

Combine like terms: 4 + -4 = 0
1 + 1x + -1x2 = 0

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

Divide each side by '-1'.
-1 + -1x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 1 + 0.25

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

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1x + x2 = 1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -0.5 = 1.118033989 Simplifying x + -0.5 = 1.118033989 Reorder the terms: -0.5 + x = 1.118033989 Solving -0.5 + x = 1.118033989 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 = 1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.118033989 + 0.5 x = 1.118033989 + 0.5 Combine like terms: 1.118033989 + 0.5 = 1.618033989 x = 1.618033989 Simplifying x = 1.618033989

Subproblem 2

x + -0.5 = -1.118033989 Simplifying x + -0.5 = -1.118033989 Reorder the terms: -0.5 + x = -1.118033989 Solving -0.5 + x = -1.118033989 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 = -1.118033989 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.118033989 + 0.5 x = -1.118033989 + 0.5 Combine like terms: -1.118033989 + 0.5 = -0.618033989 x = -0.618033989 Simplifying x = -0.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.618033989, -0.618033989}

See similar equations:

| 5c+3+2c=13 | | 51-3x=15x+19 | | 6-9x=16-16x | | 72(z-90)=z+83 | | 20+(2+r)=r | | 20+(2+r)=x | | 48-18x=9x+30 | | 64x-34=x-10 | | 4a+12b=24 | | 2x+17=3x+7 | | y+(-59)=3 | | 2x+40=9x+37 | | 2x+40=9x+7 | | 8a-4=4a+16 | | 4w^2+14w+6=0 | | (10x-25)=(15x-6) | | 37-18+8w=87 | | -4x-5y=15 | | 1+8x=31-16x | | 69(x-82)=x+58 | | 4x-(x+2)=7+2(x-3) | | x+8+2x+4= | | 7+x=2x-8 | | 4z-7z+3=9 | | 75(y-88)=y+(-47) | | 5x-15=5(x-4) | | -8k+ar=r-8y | | 15x^2-9x= | | x*x+2x+-35=0 | | An=n+1 | | 7x+0y=6 | | 4x^2+20x+25=1 |

Equations solver categories