2x^2+8x-31=0

Simple and best practice solution for 2x^2+8x-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 2x^2+8x-31=0 equation:


Simplifying
2x2 + 8x + -31 = 0

Reorder the terms:
-31 + 8x + 2x2 = 0

Solving
-31 + 8x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-15.5 + 4x + x2 = 0

Move the constant term to the right:

Add '15.5' to each side of the equation.
-15.5 + 4x + 15.5 + x2 = 0 + 15.5

Reorder the terms:
-15.5 + 15.5 + 4x + x2 = 0 + 15.5

Combine like terms: -15.5 + 15.5 = 0.0
0.0 + 4x + x2 = 0 + 15.5
4x + x2 = 0 + 15.5

Combine like terms: 0 + 15.5 = 15.5
4x + x2 = 15.5

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 = 15.5 + 4

Reorder the terms:
4 + 4x + x2 = 15.5 + 4

Combine like terms: 15.5 + 4 = 19.5
4 + 4x + x2 = 19.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 19.5

Calculate the square root of the right side: 4.415880433

Break this problem into two subproblems by setting 
(x + 2) equal to 4.415880433 and -4.415880433.

Subproblem 1

x + 2 = 4.415880433 Simplifying x + 2 = 4.415880433 Reorder the terms: 2 + x = 4.415880433 Solving 2 + x = 4.415880433 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 = 4.415880433 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.415880433 + -2 x = 4.415880433 + -2 Combine like terms: 4.415880433 + -2 = 2.415880433 x = 2.415880433 Simplifying x = 2.415880433

Subproblem 2

x + 2 = -4.415880433 Simplifying x + 2 = -4.415880433 Reorder the terms: 2 + x = -4.415880433 Solving 2 + x = -4.415880433 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 = -4.415880433 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.415880433 + -2 x = -4.415880433 + -2 Combine like terms: -4.415880433 + -2 = -6.415880433 x = -6.415880433 Simplifying x = -6.415880433

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.415880433, -6.415880433}

See similar equations:

| 2x^3-12x^2-32=0 | | -3h+1=-14 | | 2ln(3x-1)-5=0 | | 6=-1(-5-x) | | 8x-15=5x+8 | | s*5+39=164 | | 4*x^2+9*y^2+-32*x+-36*y+64=0 | | 5x+19=14x+80 | | 4x^2+9y^2+-32x+-36y+64=0 | | w-0.25w=w | | -5y+9=-41 | | w-0.25w= | | -3y+7=28 | | 1/3(12-24x)=-2(4x-2) | | 8x+2=54 | | Bs=5x-4 | | 9x-15=79.5 | | 2n+4=n+5 | | 90=x^2+9 | | -5+7=-13 | | 13(t-3)+8t=7(3t+4)-8 | | 9d-4d+3d-2=2d | | -3y=x+7 | | 15m+4=148 | | 2x+8-5x=4x-9+15 | | x^2-3x+5=y | | x+(x+2)=98 | | x(x+-5)=6 | | 8-(2x+1)=3 | | -8y=13y-17 | | 4j-3= | | 7+6(h+2)=43 |

Equations solver categories