2x^2+1=3-x

Simple and best practice solution for 2x^2+1=3-x 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^2+1=3-x equation:


Simplifying
2x2 + 1 = 3 + -1x

Reorder the terms:
1 + 2x2 = 3 + -1x

Solving
1 + 2x2 = 3 + -1x

Solving for variable 'x'.

Reorder the terms:
1 + -3 + x + 2x2 = 3 + -1x + -3 + x

Combine like terms: 1 + -3 = -2
-2 + x + 2x2 = 3 + -1x + -3 + x

Reorder the terms:
-2 + x + 2x2 = 3 + -3 + -1x + x

Combine like terms: 3 + -3 = 0
-2 + x + 2x2 = 0 + -1x + x
-2 + x + 2x2 = -1x + x

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

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

Divide each side by '2'.
-1 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5x + x2 = 0 + 1
0.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5x + x2 = 1

The x term is x.  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.
0.5x + 0.25 + x2 = 1 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + 0.5x + 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 = 0.618033989 x = 0.618033989 Simplifying x = 0.618033989

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 = -1.618033989 x = -1.618033989 Simplifying x = -1.618033989

Solution

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

See similar equations:

| 7n-n=18 | | (-4x^3+10x^2-7x+5)+(7x^3+6x^2-8x-3)= | | [2x+x^2]=1 | | Y=1.25x+30 | | 4(4x-(7-4y+5x)+3y)= | | 2zy/y=14/y | | 2ab/21xy*14xy | | 5(x-2)=-(x+6) | | 2(x+-14)+3(3x+5)= | | 3x+14=4x-6 | | 4/5x3/5= | | 7n-23=-25+5n | | -1/2x=32 | | -x-12=-7x+3x | | 8a+8b-2a= | | 6(6x-6)+5=-31 | | -2(1+6n)=10 | | X^2-12+3=0 | | -21z^6+49z^4-9z^2=0 | | 5z-17=-9+6z | | 4g(-1)= | | y+4/y-1=-4/3 | | -9m+69-6m+12=5m-2m-7-4m+4 | | -6x-3(-2x-1)=-15 | | x+5=1/3(6x-5) | | 6+k-7-1=-8+3k | | 7x+6=-2+7x-4+7x | | 8[5-(6x-7)]+8x=0 | | -48-34= | | -257=-6(-5-7x)-x | | X=450+-5x | | -84=-6+6(1-2n) |

Equations solver categories