x+x^2=2.15

Simple and best practice solution for x+x^2=2.15 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^2=2.15 equation: 


Simplifying
x + x2 = 2.15

Solving
x + x2 = 2.15

Solving for variable 'x'.

Reorder the terms:
-2.15 + x + x2 = 2.15 + -2.15

Combine like terms: 2.15 + -2.15 = 0.00
-2.15 + x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '2.15' to each side of the equation.
-2.15 + x + 2.15 + x2 = 0.00 + 2.15

Reorder the terms:
-2.15 + 2.15 + x + x2 = 0.00 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x + x2 = 0.00 + 2.15
x + x2 = 0.00 + 2.15

Combine like terms: 0.00 + 2.15 = 2.15
x + x2 = 2.15

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.
x + 0.25 + x2 = 2.15 + 0.25

Reorder the terms:
0.25 + x + x2 = 2.15 + 0.25

Combine like terms: 2.15 + 0.25 = 2.4
0.25 + x + x2 = 2.4

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.4

Calculate the square root of the right side: 1.549193338

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.549193338 and -1.549193338.


Subproblem 1
x + 0.5 = 1.549193338

Simplifying
x + 0.5 = 1.549193338

Reorder the terms:
0.5 + x = 1.549193338

Solving
0.5 + x = 1.549193338

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 = 1.549193338 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.549193338 + -0.5
x = 1.549193338 + -0.5

Combine like terms: 1.549193338 + -0.5 = 1.049193338
x = 1.049193338

Simplifying
x = 1.049193338


Subproblem 2
x + 0.5 = -1.549193338

Simplifying
x + 0.5 = -1.549193338

Reorder the terms:
0.5 + x = -1.549193338

Solving
0.5 + x = -1.549193338

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 = -1.549193338 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.549193338 + -0.5
x = -1.549193338 + -0.5

Combine like terms: -1.549193338 + -0.5 = -2.049193338
x = -2.049193338

Simplifying
x = -2.049193338


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.049193338, -2.049193338}

See similar equations:

| x+x^2=2.4 | | 3m=81m | | y=x^2-2b | | 5(2x+3)=2x-(3x+4) | | y^4+y^2+6=0 | | y+y^2=2.16 | | 3x-12=7x-4 | | 2.8-4x=0 | | 2+3z=9 | | p(-1/16p) | | ln(3x-2)=-4cos(0.5x)+1 | | z^6-2z^3-1=0 | | x^2+x(2-i)+3-i=0 | | 6(y+5)=18 | | 6=30-2*x | | 6=30-2x | | 9(2h+3)= | | -27x=77 | | 5x^2-35x-60=0 | | 81-27x=4 | | 3x-30=2x-5 | | (X*.40)+X=75 | | x^2+19xy+48y^2=0 | | l=0.32t+40 | | 3-18x+24=0 | | x=(3x-45)+4 | | z^3+3z^2+9z+7=0 | | 8-k=12 | | 37x+29y=1000 | | x-5=12+8 | | log(4x+3)+logx=1 | | 33=3(x-4) |

Equations solver categories