4x+x^2=11

Simple and best practice solution for 4x+x^2=11 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 4x+x^2=11 equation:


Simplifying
4x + x2 = 11

Solving
4x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
-11 + 4x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 4x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + 4x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 4x + x2 = 0 + 11
4x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
4x + x2 = 11

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 11 + 4

Reorder the terms:
4 + 4x + x2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + 4x + x2 = 15

Factor a perfect square on the left side:
(x + 2)(x + 2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(x + 2) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + 2 = 3.872983346 Simplifying x + 2 = 3.872983346 Reorder the terms: 2 + x = 3.872983346 Solving 2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.872983346 + -2 x = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 x = 1.872983346 Simplifying x = 1.872983346

Subproblem 2

x + 2 = -3.872983346 Simplifying x + 2 = -3.872983346 Reorder the terms: 2 + x = -3.872983346 Solving 2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.872983346 + -2 x = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 x = -5.872983346 Simplifying x = -5.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.872983346, -5.872983346}

See similar equations:

| -2x-7y=9 | | V-9.8=13.2 | | 8t^2+22t-21=0 | | M-9.9=.1 | | -97-7x=2x+101 | | 2-[3(x+4)+5x]=54 | | T+6.4=10.2 | | -2x+2y=18 | | 6p^2-p-35=0 | | 4(6ax+y)=23ax-3y | | (3y+2)(y+2)=0 | | 17-r/r+8=-2/-3 | | x/z | | 2n^2+5n-102=0 | | 6g+1.9=50.5 | | 3x-5x-11=-2x+3-11 | | -2x^2-14x+5=0 | | 2(3ax+y)=5ax-5y | | S/1.4=12 | | N-5*10=20 | | x^3-7x^2-8x-12=0 | | N-10*2=16 | | 2(2x+3)/5 | | y/23=-2.5 | | 0.02(y-4)+0.16y=0.20y-0.01(20) | | 7x+3=19-x | | 341=d | | b-1+3b=24 | | 5c(c-2)=6+3c | | -4.3k=21.5 | | y=-2-3x | | 3s^2-24= |

Equations solver categories