x^2+22x=31

Simple and best practice solution for x^2+22x=31 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=31 equation:


Simplifying
x2 + 22x = 31

Reorder the terms:
22x + x2 = 31

Solving
22x + x2 = 31

Solving for variable 'x'.

Reorder the terms:
-31 + 22x + x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 22x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 22x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 22x + x2 = 0 + 31
22x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
22x + x2 = 31

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 = 31 + 121

Reorder the terms:
121 + 22x + x2 = 31 + 121

Combine like terms: 31 + 121 = 152
121 + 22x + x2 = 152

Factor a perfect square on the left side:
(x + 11)(x + 11) = 152

Calculate the square root of the right side: 12.328828006

Break this problem into two subproblems by setting 
(x + 11) equal to 12.328828006 and -12.328828006.

Subproblem 1

x + 11 = 12.328828006 Simplifying x + 11 = 12.328828006 Reorder the terms: 11 + x = 12.328828006 Solving 11 + x = 12.328828006 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 = 12.328828006 + -11 Combine like terms: 11 + -11 = 0 0 + x = 12.328828006 + -11 x = 12.328828006 + -11 Combine like terms: 12.328828006 + -11 = 1.328828006 x = 1.328828006 Simplifying x = 1.328828006

Subproblem 2

x + 11 = -12.328828006 Simplifying x + 11 = -12.328828006 Reorder the terms: 11 + x = -12.328828006 Solving 11 + x = -12.328828006 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 = -12.328828006 + -11 Combine like terms: 11 + -11 = 0 0 + x = -12.328828006 + -11 x = -12.328828006 + -11 Combine like terms: -12.328828006 + -11 = -23.328828006 x = -23.328828006 Simplifying x = -23.328828006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.328828006, -23.328828006}

See similar equations:

| 4(3w+3)+2w=7(w+7)-16 | | 3y^2+7y=10 | | 3r+2s= | | 2.4(v-1.4)=3.6(-v+2.8) | | 4p+5=7+3p | | 0.5x-0.4(3)=1.8 | | y=abs(x+2)-2 | | (-7)(-2)= | | -3x+2y=16 | | 2*(-9)= | | j+16-148+4= | | 15-6x-x^2=y | | 8x-7=7x+9 | | m-13+4-6= | | x^4+2x^3-3x^2-4x+4=0 | | 10+3= | | 7.9x+4=6.9x | | -7+3y+9+2y= | | 63+b=90 | | 4(3x-2)=15 | | 48*5=X | | 48*5= | | {7x-2}+5=3 | | 11x-20+7x+28=180 | | 3x+134+6x+10=180 | | -7x-5y=-4 | | 11x-20+7x+20=180 | | 4x-3-8=8 | | 2y+3x=1 | | X^2-11-448=0 | | 3x+4=2(x-3) | | .5y-6x=1 |

Equations solver categories