4x^2-180x-400=0

Simple and best practice solution for 4x^2-180x-400=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 4x^2-180x-400=0 equation: 


Simplifying
4x2 + -180x + -400 = 0

Reorder the terms:
-400 + -180x + 4x2 = 0

Solving
-400 + -180x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-100 + -45x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-100 + -45x + x2)' equal to zero and attempt to solve:

Simplifying
-100 + -45x + x2 = 0

Solving
-100 + -45x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + -45x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + -45x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -45x + x2 = 0 + 100
-45x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
-45x + x2 = 100

The x term is -45x.  Take half its coefficient (-22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
-45x + 506.25 + x2 = 100 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 100 + 506.25

Combine like terms: 100 + 506.25 = 606.25
506.25 + -45x + x2 = 606.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + -22.5) equal to 24.622144504 and -24.622144504.


Subproblem 1
x + -22.5 = 24.622144504

Simplifying
x + -22.5 = 24.622144504

Reorder the terms:
-22.5 + x = 24.622144504

Solving
-22.5 + x = 24.622144504

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = 24.622144504 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 24.622144504 + 22.5
x = 24.622144504 + 22.5

Combine like terms: 24.622144504 + 22.5 = 47.122144504
x = 47.122144504

Simplifying
x = 47.122144504


Subproblem 2
x + -22.5 = -24.622144504

Simplifying
x + -22.5 = -24.622144504

Reorder the terms:
-22.5 + x = -24.622144504

Solving
-22.5 + x = -24.622144504

Solving for variable 'x'.

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

Add '22.5' to each side of the equation.
-22.5 + 22.5 + x = -24.622144504 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -24.622144504 + 22.5
x = -24.622144504 + 22.5

Combine like terms: -24.622144504 + 22.5 = -2.122144504
x = -2.122144504

Simplifying
x = -2.122144504


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.122144504, -2.122144504}
Solution
x = {47.122144504, -2.122144504}

See similar equations:

| x^3-27x^2-120x-124=0 | | 25.12=1/3(12.56x) | | 5(x+1)-7=3(-1)+2x | | y+5z=27 | | u+6x=11 | | x^3+3x=200 | | x-15.99=58.06 | | 2x+2x=y+5 | | ln(19)+ln(x)=x | | .14x+.06(3000-x)=580 | | 5u+6z=28 | | .65x+.1x=x-10 | | 81-3x-6+2x=36-36x+54 | | 34.7=6.4-3.7 | | 5u+4x=36 | | A=1/2(25)(18) | | 5u+6y=55 | | 36*9-3x-6+2x=36-36x+18*3 | | 95x+33=-15x-19 | | 34.7=6.4x-3.7 | | 5x-10=3(x-2) | | 5x-5=1(2x-1) | | 16x^2-44x+24=0 | | 4x-28=64+2x | | -42x^2+50x+8=0 | | (5a/9)-(a/5)=16/3 | | 6x-2=2(2x-6) | | 8+5q=3 | | -28x^2+17x+6=0 | | 3x-11=37-x | | 10*x=4.9966 | | x^4/5-81=0 |

Equations solver categories