x^2+10x=31

Simple and best practice solution for x^2+10x=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+10x=31 equation:


Simplifying
x2 + 10x = 31

Reorder the terms:
10x + x2 = 31

Solving
10x + x2 = 31

Solving for variable 'x'.

Reorder the terms:
-31 + 10x + x2 = 31 + -31

Combine like terms: 31 + -31 = 0
-31 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 10x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 10x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 10x + x2 = 0 + 31
10x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
10x + x2 = 31

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 31 + 25

Reorder the terms:
25 + 10x + x2 = 31 + 25

Combine like terms: 31 + 25 = 56
25 + 10x + x2 = 56

Factor a perfect square on the left side:
(x + 5)(x + 5) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(x + 5) equal to 7.483314774 and -7.483314774.

Subproblem 1

x + 5 = 7.483314774 Simplifying x + 5 = 7.483314774 Reorder the terms: 5 + x = 7.483314774 Solving 5 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.483314774 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.483314774 + -5 x = 7.483314774 + -5 Combine like terms: 7.483314774 + -5 = 2.483314774 x = 2.483314774 Simplifying x = 2.483314774

Subproblem 2

x + 5 = -7.483314774 Simplifying x + 5 = -7.483314774 Reorder the terms: 5 + x = -7.483314774 Solving 5 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.483314774 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.483314774 + -5 x = -7.483314774 + -5 Combine like terms: -7.483314774 + -5 = -12.483314774 x = -12.483314774 Simplifying x = -12.483314774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.483314774, -12.483314774}

See similar equations:

| x^2+12x=5 | | x^2+26x=68 | | 2x+7y=-8 | | 9y-7=5y+1 | | x=300-y | | 2x+2y=600 | | x^2+y^2-10x+6y+14=0 | | x^2-44x+483=0 | | 6=n^2-n | | x^2+x-5=3 | | 4a+2b=110 | | =10x+9 | | 2x+2=x-2 | | 8X^2-80=0 | | (3x)2-27= | | 9-3y-11y=12y-8 | | w=2w^2+1 | | 2t=60-t | | 2x^2+3x-180=0 | | x-29+3x=-6x-22-3x | | 3(7b-2)=-69 | | 2x+10=7x-11 | | 4k+39=7k+6 | | 4x+3y=73 | | x=20+4y | | 10X^5*Y^4*5X^3*Y^2=0 | | 10X^5*Y^4=0 | | 48x-16=0 | | y-10.2=-6.5+7.8 | | x^2+2*x=12 | | -4x^2+6x+40=0 | | 4-10-6x+7x-9x=-12x |

Equations solver categories