x^2+4x-31=0

Simple and best practice solution for x^2+4x-31=0 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+4x-31=0 equation:


Simplifying
x2 + 4x + -31 = 0

Reorder the terms:
-31 + 4x + x2 = 0

Solving
-31 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + 4x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + 4x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + 4x + x2 = 0 + 31
4x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
4x + x2 = 31

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 = 31 + 4

Reorder the terms:
4 + 4x + x2 = 31 + 4

Combine like terms: 31 + 4 = 35
4 + 4x + x2 = 35

Factor a perfect square on the left side:
(x + 2)(x + 2) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + 2) equal to 5.916079783 and -5.916079783.

Subproblem 1

x + 2 = 5.916079783 Simplifying x + 2 = 5.916079783 Reorder the terms: 2 + x = 5.916079783 Solving 2 + x = 5.916079783 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 = 5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.916079783 + -2 x = 5.916079783 + -2 Combine like terms: 5.916079783 + -2 = 3.916079783 x = 3.916079783 Simplifying x = 3.916079783

Subproblem 2

x + 2 = -5.916079783 Simplifying x + 2 = -5.916079783 Reorder the terms: 2 + x = -5.916079783 Solving 2 + x = -5.916079783 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 = -5.916079783 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.916079783 + -2 x = -5.916079783 + -2 Combine like terms: -5.916079783 + -2 = -7.916079783 x = -7.916079783 Simplifying x = -7.916079783

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.916079783, -7.916079783}

See similar equations:

| 7-4.9t=15t+7.6t | | 18p+6=24p-42 | | 5x+5y+30z=0 | | -15=5x+1 | | 6x-12=-2x+8 | | 3(2x+1)=4 | | 28x^5+22x^3+15x^2= | | 3w+5x-15y+7w+7x+9y= | | sinx=.4 | | 4x+3x^2=14 | | 2x+64-100=0 | | 16=a(a)+-6a | | Lny=2.8 | | 2.8=lnX | | -2xy^3(3y^6+6x^4-8)= | | 9x+10y=1 | | 3+2ln(x)=5 | | n-1=4n-7 | | n/9=6-n | | 45x^2-3=-7 | | 25x=y+5 | | 10y^2-17y-20=0 | | x+0.20x=549.60 | | 2cos(x)+sqrt(2)=0 | | x^3-5x^2+3x-1=0 | | 35-7p=0 | | 9n+2m= | | -2*log(5)x-19=-23 | | -5(-x)= | | h(x)=x^2+4 | | 2y-1=0 | | x-(x*.3)=18 |

Equations solver categories