x^2-3x-209=0

Simple and best practice solution for x^2-3x-209=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^2-3x-209=0 equation: 


Simplifying
x2 + -3x + -209 = 0

Reorder the terms:
-209 + -3x + x2 = 0

Solving
-209 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '209' to each side of the equation.
-209 + -3x + 209 + x2 = 0 + 209

Reorder the terms:
-209 + 209 + -3x + x2 = 0 + 209

Combine like terms: -209 + 209 = 0
0 + -3x + x2 = 0 + 209
-3x + x2 = 0 + 209

Combine like terms: 0 + 209 = 209
-3x + x2 = 209

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 209 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 209 + 2.25

Combine like terms: 209 + 2.25 = 211.25
2.25 + -3x + x2 = 211.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 211.25

Calculate the square root of the right side: 14.534441854

Break this problem into two subproblems by setting 
(x + -1.5) equal to 14.534441854 and -14.534441854.


Subproblem 1
x + -1.5 = 14.534441854

Simplifying
x + -1.5 = 14.534441854

Reorder the terms:
-1.5 + x = 14.534441854

Solving
-1.5 + x = 14.534441854

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 14.534441854 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 14.534441854 + 1.5
x = 14.534441854 + 1.5

Combine like terms: 14.534441854 + 1.5 = 16.034441854
x = 16.034441854

Simplifying
x = 16.034441854


Subproblem 2
x + -1.5 = -14.534441854

Simplifying
x + -1.5 = -14.534441854

Reorder the terms:
-1.5 + x = -14.534441854

Solving
-1.5 + x = -14.534441854

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -14.534441854 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -14.534441854 + 1.5
x = -14.534441854 + 1.5

Combine like terms: -14.534441854 + 1.5 = -13.034441854
x = -13.034441854

Simplifying
x = -13.034441854


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.034441854, -13.034441854}

See similar equations:

| (x^2+3x+2)/(x^2-x-2) | | 7y+3y(2y-4)= | | 5-6=7w | | 5=6x-y | | -6a^4b^-3c^2/-2a^-2b^-2c^-2 | | (4x+3x)+6=92 | | 3x^4-3x^2-6=0 | | y-x^2=-6x-7 | | z-22=-26 | | x-0.17x= | | -4(m-7)=2m-8 | | -47(x-37)=x+32 | | 5(x+7)=-2x-10 | | 0.0(x+300)=0.06x-205 | | 5-487(x-37)=x+32 | | 15p+18q= | | 4x^3-3x^2-16x+2=0 | | 4x+5+2x+20+5x-10=180 | | (4x+3)+6=92 | | 5/2x-1=x+1/4 | | 35000+1680x=175000+550+x | | 79(x-55)=x+8 | | P=b+a+3cforb | | 6.7-(-7.6)= | | w+6=1 | | 3+3g=-14 | | 26/3-23/5 | | 4(2x+6)/8-2(5x-10)/5=0 | | 32-4x=32 | | y-2+50=-28 | | 0+8y=8 | | 3/5x-14=-8 |

Equations solver categories