x^2+13.5x+12=0

Simple and best practice solution for x^2+13.5x+12=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+13.5x+12=0 equation: 


Simplifying
x2 + 13.5x + 12 = 0

Reorder the terms:
12 + 13.5x + x2 = 0

Solving
12 + 13.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 13.5x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 13.5x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 13.5x + x2 = 0 + -12
13.5x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
13.5x + x2 = -12

The x term is 13.5x.  Take half its coefficient (6.75).
Square it (45.5625) and add it to both sides.

Add '45.5625' to each side of the equation.
13.5x + 45.5625 + x2 = -12 + 45.5625

Reorder the terms:
45.5625 + 13.5x + x2 = -12 + 45.5625

Combine like terms: -12 + 45.5625 = 33.5625
45.5625 + 13.5x + x2 = 33.5625

Factor a perfect square on the left side:
(x + 6.75)(x + 6.75) = 33.5625

Calculate the square root of the right side: 5.793315113

Break this problem into two subproblems by setting 
(x + 6.75) equal to 5.793315113 and -5.793315113.


Subproblem 1
x + 6.75 = 5.793315113

Simplifying
x + 6.75 = 5.793315113

Reorder the terms:
6.75 + x = 5.793315113

Solving
6.75 + x = 5.793315113

Solving for variable 'x'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + x = 5.793315113 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = 5.793315113 + -6.75
x = 5.793315113 + -6.75

Combine like terms: 5.793315113 + -6.75 = -0.956684887
x = -0.956684887

Simplifying
x = -0.956684887


Subproblem 2
x + 6.75 = -5.793315113

Simplifying
x + 6.75 = -5.793315113

Reorder the terms:
6.75 + x = -5.793315113

Solving
6.75 + x = -5.793315113

Solving for variable 'x'.

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

Add '-6.75' to each side of the equation.
6.75 + -6.75 + x = -5.793315113 + -6.75

Combine like terms: 6.75 + -6.75 = 0.00
0.00 + x = -5.793315113 + -6.75
x = -5.793315113 + -6.75

Combine like terms: -5.793315113 + -6.75 = -12.543315113
x = -12.543315113

Simplifying
x = -12.543315113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.956684887, -12.543315113}

See similar equations:

| (-3v+3w)/-4=(9v+x)/6 | | 7/4(8/5) | | 7d=38 | | 7/4(5/8) | | 26+m=14 | | x^2+13.5+12=0 | | -12+50/(-2-3)+72/(4+2) | | 5(b-5)= | | t-1/3=5-1 | | (5r-3)(r-1)=0 | | -4x-6=1 | | (5/3x)+(2/x)=1 | | 5/3+2/x=1 | | 4x^5-24x^4+8x^3=0 | | x^2+300x=15000 | | 6-10x=75-31x | | (5/3)+(2/x)=1 | | 40=0.4x+0.2x^2 | | 40=0.4x | | x-407/4=15/4 | | 3x^2+y^2=36 | | 41-6x=12x+17 | | -5h-1=-21 | | (9-4x^2)/(4x-20)*(24x^2-6x^3)/(2x^2-5x-12) | | 2x^2-14x+45=0 | | 3mn+6m+7mn= | | -324-72c=-225+90c | | x-2.2=7.6 | | 7(n+1)+4(n+7)= | | -5h-1=21 | | -3x+12=2x-3 | | B-1=-2(x+5) |

Equations solver categories