x*x=x+1

Simple and best practice solution for x*x=x+1 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*x=x+1 equation:


Simplifying
x * x = x + 1

Multiply x * x
x2 = x + 1

Reorder the terms:
x2 = 1 + x

Solving
x2 = 1 + x

Solving for variable 'x'.

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

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

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

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

Begin completing the square.

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:

| M(m-14)=-48 | | 1/4(8x-12)=1/3(9x-6) | | 176=(x+3)(x+3)x-1 | | 12x^7-40x^6-32x^5=0 | | 1+90=20+9x | | -3(y-9)=-5y+39 | | -6(p+2)-p-4=-7(p+3)+5 | | 3(5x+3)=22(3x+18) | | 7x+35=35+14 | | x-5x-20=6x+30 | | 2.5t=2+1.5t | | 4(3x-0.4)=5x-1.6 | | 0.75x+0.05(6-x)=0.10(-39) | | 2x+-2=4x | | 225=x+(x+47) | | 4x+9(7)=11 | | 4x-2=88-6 | | 0.15x+0.05(14-x)=0.10(5) | | 5(2m+5n)= | | 4(0)+9y=11 | | 0.25x+0.05(16-x)=0.10(32) | | x-14/.28= | | y=-0.1(x-30)2+90 | | x-14/.28 | | -7(2x+1)+(5x-4)=0 | | p=-q^2+6000 | | -12x+7=5x | | .07x=40 | | 6-6x-2=-37+3x-13 | | 48-(6x+7)=2(x+7)+x | | 2x^2+3x+350=0 | | -6x-12=2x+20 |

Equations solver categories