2x+x^2=1

Simple and best practice solution for 2x+x^2=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 2x+x^2=1 equation:


Simplifying
2x + x2 = 1

Solving
2x + x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 2x + x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2x + x2 = 0 + 1
2x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2x + x2 = 1

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1 + 1

Reorder the terms:
1 + 2x + x2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2x + x2 = 2

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + 1 = 1.414213562 Simplifying x + 1 = 1.414213562 Reorder the terms: 1 + x = 1.414213562 Solving 1 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.414213562 + -1 x = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x = 0.414213562 Simplifying x = 0.414213562

Subproblem 2

x + 1 = -1.414213562 Simplifying x + 1 = -1.414213562 Reorder the terms: 1 + x = -1.414213562 Solving 1 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.414213562 + -1 x = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x = -2.414213562 Simplifying x = -2.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.414213562, -2.414213562}

See similar equations:

| 7x^2+16x+4= | | 2x+x^2+1= | | 80x+320=7208+(-220x) | | -7.5-5.5(1+5v)=-21.5 | | 4(p+1)+3p=29+2p | | -4x+10=60 | | 10w+7=8(2w-4)-9 | | 5/9x^5-5/4^3 | | (-5)/(2x)=()/(2x^7) | | 30.5+9.5d=6(2.5d+8.5) | | 36x^2+75x+36=0 | | 12=-3/8w | | -2(10-3y)=7y+2y | | x^2+24x+c=o | | (6a-5d)-(3a-2d)=0 | | 5+11i=7(5-2t) | | 45/3= | | x^2-19x+c=0 | | 18n=1n^2 | | -8x=54 | | 12-(1/5) | | 3(x+14)=18 | | 12-1/5 | | 2x-(-3+9-1)+2=x-(-3) | | 7lnx=y | | 6x+6=9x-12 | | x/6=9.9 | | solvex^4+2x^3-15x^2-36x=0 | | 3-(6u-7)=4u-2 | | 0.4x=52 | | 0=-[x]+2 | | 3xy/2x×4xy |

Equations solver categories