2x^2+16x+31=

Simple and best practice solution for 2x^2+16x+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 2x^2+16x+31= equation:


Simplifying
2x2 + 16x + 31 = 0

Reorder the terms:
31 + 16x + 2x2 = 0

Solving
31 + 16x + 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 + 8x + x2 = 0

Move the constant term to the right:

Add '-15.5' to each side of the equation.
15.5 + 8x + -15.5 + x2 = 0 + -15.5

Reorder the terms:
15.5 + -15.5 + 8x + x2 = 0 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + 8x + x2 = 0 + -15.5
8x + x2 = 0 + -15.5

Combine like terms: 0 + -15.5 = -15.5
8x + x2 = -15.5

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -15.5 + 16

Reorder the terms:
16 + 8x + x2 = -15.5 + 16

Combine like terms: -15.5 + 16 = 0.5
16 + 8x + x2 = 0.5

Factor a perfect square on the left side:
(x + 4)(x + 4) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 4) equal to 0.707106781 and -0.707106781.

Subproblem 1

x + 4 = 0.707106781 Simplifying x + 4 = 0.707106781 Reorder the terms: 4 + x = 0.707106781 Solving 4 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0.707106781 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.707106781 + -4 x = 0.707106781 + -4 Combine like terms: 0.707106781 + -4 = -3.292893219 x = -3.292893219 Simplifying x = -3.292893219

Subproblem 2

x + 4 = -0.707106781 Simplifying x + 4 = -0.707106781 Reorder the terms: 4 + x = -0.707106781 Solving 4 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -0.707106781 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.707106781 + -4 x = -0.707106781 + -4 Combine like terms: -0.707106781 + -4 = -4.707106781 x = -4.707106781 Simplifying x = -4.707106781

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.292893219, -4.707106781}

See similar equations:

| -1/9-5/3v=3/2 | | 7x-2=8x-37 | | 5c-2c=55 | | 0.5x+15-0.2x=30 | | 7x+6+10=3 | | 7x+14=120 | | -6/10x+3x=1/3x+62/3 | | 4x^2-22x+31=0 | | (11n+n)+5n= | | n^2=0.6 | | 7x-11=5x-9 | | e^5x+2=e^3x+12 | | log(2x-2)-log(x-1)=log(x) | | 7+3lnx=5 | | (11n-n)+5n= | | 8z+52=28 | | 8z=-29 | | 287954-x=71754 | | 0.60x+0.05(14-x)=0.10(-48) | | 7n^2-4=0 | | 4x^2-40x=-94 | | f(x)=x^2+5x-14 | | 7/3*2/1+1/1 | | f(x)=x^2+5x-15 | | (19b-4)-6(3b+1)=-5 | | h=32t-5t^2 | | 4n^3+24n^2-49n-294=0 | | 12y+57=33 | | 0=5x^2+7x+9 | | -3x^2=-5x+13 | | x^2+3x-4x+12= | | .06x-.01y=1.9 |

Equations solver categories