2x^2+31x+7.5=0

Simple and best practice solution for 2x^2+31x+7.5=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+31x+7.5=0 equation: 


Simplifying
2x2 + 31x + 7.5 = 0

Reorder the terms:
7.5 + 31x + 2x2 = 0

Solving
7.5 + 31x + 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'.
3.75 + 15.5x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 15.5x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 15.5x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 15.5x + x2 = 0 + -3.75
15.5x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
15.5x + x2 = -3.75

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = -3.75 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = -3.75 + 60.0625

Combine like terms: -3.75 + 60.0625 = 56.3125
60.0625 + 15.5x + x2 = 56.3125

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 56.3125

Calculate the square root of the right side: 7.50416551

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.50416551 and -7.50416551.


Subproblem 1
x + 7.75 = 7.50416551

Simplifying
x + 7.75 = 7.50416551

Reorder the terms:
7.75 + x = 7.50416551

Solving
7.75 + x = 7.50416551

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 7.50416551 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 7.50416551 + -7.75
x = 7.50416551 + -7.75

Combine like terms: 7.50416551 + -7.75 = -0.24583449
x = -0.24583449

Simplifying
x = -0.24583449


Subproblem 2
x + 7.75 = -7.50416551

Simplifying
x + 7.75 = -7.50416551

Reorder the terms:
7.75 + x = -7.50416551

Solving
7.75 + x = -7.50416551

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -7.50416551 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -7.50416551 + -7.75
x = -7.50416551 + -7.75

Combine like terms: -7.50416551 + -7.75 = -15.25416551
x = -15.25416551

Simplifying
x = -15.25416551


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.24583449, -15.25416551}

See similar equations:

| -8=-(x+8) | | y=-1/3-15 | | a^2-5a-18=-4 | | a(a-5)=-6(a-7) | | 1.375(n-10)=64 | | 5p-14=8p+16 | | 3x-7x+7x-4= | | (2-u)(5u+9)=9 | | (x+8)+64=90 | | -20=x/4-13 | | 84=q+60 | | x/2+3=22 | | 12-(2+4)*33= | | 4t^2+4t-9=o | | 80b^3+52b^2-60b= | | y-(4y-7)=5y-(y+21) | | b^2-3b+19= | | 2n/3-6/13=60/39 | | 2(3-2x)=9(10-8x) | | 5=g/8 | | (a+1)(2a+5)=(2a+3)(a-4)+5 | | g-27=27-10g | | t^4+37t^2+36= | | 9(6.4+0.8y)-y=33 | | 6p^6-11p^3+4r^2= | | 28793=45*ln(x)-x | | 2+10x=-7(-8) | | 10+5z+10=4z+1 | | t=35+7+14 | | -2x+21/2=-6x+11/6 | | 3-5/3= | | 3705=x(57) |

Equations solver categories