x^2+22x=416

Simple and best practice solution for x^2+22x=416 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^2+22x=416 equation:


Simplifying
x2 + 22x = 416

Reorder the terms:
22x + x2 = 416

Solving
22x + x2 = 416

Solving for variable 'x'.

Reorder the terms:
-416 + 22x + x2 = 416 + -416

Combine like terms: 416 + -416 = 0
-416 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '416' to each side of the equation.
-416 + 22x + 416 + x2 = 0 + 416

Reorder the terms:
-416 + 416 + 22x + x2 = 0 + 416

Combine like terms: -416 + 416 = 0
0 + 22x + x2 = 0 + 416
22x + x2 = 0 + 416

Combine like terms: 0 + 416 = 416
22x + x2 = 416

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 416 + 121

Reorder the terms:
121 + 22x + x2 = 416 + 121

Combine like terms: 416 + 121 = 537
121 + 22x + x2 = 537

Factor a perfect square on the left side:
(x + 11)(x + 11) = 537

Calculate the square root of the right side: 23.173260453

Break this problem into two subproblems by setting 
(x + 11) equal to 23.173260453 and -23.173260453.

Subproblem 1

x + 11 = 23.173260453 Simplifying x + 11 = 23.173260453 Reorder the terms: 11 + x = 23.173260453 Solving 11 + x = 23.173260453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 23.173260453 + -11 Combine like terms: 11 + -11 = 0 0 + x = 23.173260453 + -11 x = 23.173260453 + -11 Combine like terms: 23.173260453 + -11 = 12.173260453 x = 12.173260453 Simplifying x = 12.173260453

Subproblem 2

x + 11 = -23.173260453 Simplifying x + 11 = -23.173260453 Reorder the terms: 11 + x = -23.173260453 Solving 11 + x = -23.173260453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -23.173260453 + -11 Combine like terms: 11 + -11 = 0 0 + x = -23.173260453 + -11 x = -23.173260453 + -11 Combine like terms: -23.173260453 + -11 = -34.173260453 x = -34.173260453 Simplifying x = -34.173260453

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.173260453, -34.173260453}

See similar equations:

| 5x-6=4.5x-2 | | 3x+7-3=10x+2x-4 | | 7x+5+19=180 | | ln(4)+ln(x)=0 | | x+(x+5)+(x+11)=55 | | 2y=3(3y-5) | | 1=7/8y=4.5 | | 4x+12-9x=17-17x+12x-5 | | 2x+(1+x)3=4(x-1) | | 4*x=y/3 | | 6x-3y=20+8y | | 11=(q) | | x-2=-9x+108 | | 2+5=-3x | | (m)=3 | | 2z-1=80 | | -4/14 | | 3y+5.2=2.5 | | 5y-8y=-5 | | 20+16+10=180 | | 0=-7x+4-5x | | S+9=19 | | 4t+9+(2t+7)+6= | | 20+16+10= | | 3/4g=-10 | | 14/-4 | | 2x-8x+1=43 | | 7x^2-1=9 | | 3(d+2)=15 | | x=180-2y-30 | | 2x^3+9x^2-17x-84=0 | | -5(-7x+8)=380 |

Equations solver categories