4x^2-54x-210=0

Simple and best practice solution for 4x^2-54x-210=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^2-54x-210=0 equation: 


Simplifying
4x2 + -54x + -210 = 0

Reorder the terms:
-210 + -54x + 4x2 = 0

Solving
-210 + -54x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-105 + -27x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-105 + -27x + 2x2)' equal to zero and attempt to solve:

Simplifying
-105 + -27x + 2x2 = 0

Solving
-105 + -27x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-52.5 + -13.5x + x2 = 0

Move the constant term to the right:

Add '52.5' to each side of the equation.
-52.5 + -13.5x + 52.5 + x2 = 0 + 52.5

Reorder the terms:
-52.5 + 52.5 + -13.5x + x2 = 0 + 52.5

Combine like terms: -52.5 + 52.5 = 0.0
0.0 + -13.5x + x2 = 0 + 52.5
-13.5x + x2 = 0 + 52.5

Combine like terms: 0 + 52.5 = 52.5
-13.5x + x2 = 52.5

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 = 52.5 + 45.5625

Reorder the terms:
45.5625 + -13.5x + x2 = 52.5 + 45.5625

Combine like terms: 52.5 + 45.5625 = 98.0625
45.5625 + -13.5x + x2 = 98.0625

Factor a perfect square on the left side:
(x + -6.75)(x + -6.75) = 98.0625

Calculate the square root of the right side: 9.90265116

Break this problem into two subproblems by setting 
(x + -6.75) equal to 9.90265116 and -9.90265116.


Subproblem 1
x + -6.75 = 9.90265116

Simplifying
x + -6.75 = 9.90265116

Reorder the terms:
-6.75 + x = 9.90265116

Solving
-6.75 + x = 9.90265116

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 = 9.90265116 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = 9.90265116 + 6.75
x = 9.90265116 + 6.75

Combine like terms: 9.90265116 + 6.75 = 16.65265116
x = 16.65265116

Simplifying
x = 16.65265116


Subproblem 2
x + -6.75 = -9.90265116

Simplifying
x + -6.75 = -9.90265116

Reorder the terms:
-6.75 + x = -9.90265116

Solving
-6.75 + x = -9.90265116

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 = -9.90265116 + 6.75

Combine like terms: -6.75 + 6.75 = 0.00
0.00 + x = -9.90265116 + 6.75
x = -9.90265116 + 6.75

Combine like terms: -9.90265116 + 6.75 = -3.15265116
x = -3.15265116

Simplifying
x = -3.15265116


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.65265116, -3.15265116}
Solution
x = {16.65265116, -3.15265116}

See similar equations:

| 3/5(2m-10)=2/3+10 | | -85=5(1-3n) | | 4n-14=-8+n | | 5-10w+8w= | | 4/5=-47g | | 2m+8=28 | | 19=2k-4k | | 5x+10=-8+7x | | -1(v-4)+4(2v-9)=3 | | x-5/16=-7/8 | | 9/10+(-32/3) | | l-4+12-(-10)l=0 | | 1.3e=-4.82 | | -5(x-3)-4x=87 | | -5=19-x/7 | | 10(40-x)+5x=290 | | x/5-x/3=4 | | 2z=-16 | | .25m+12.95=21.20 | | 4t=1/4 | | 4/3e=-4.82 | | 0=x^2-40x+800 | | 2(2y-3)=10 | | x-3x+10=-x+4 | | n/12=n/3-5/4 | | 2(2y-3)=20 | | 171=-6(-4x+3)-3 | | 0=x^2-40+800 | | -3/18n=12 | | -8=.1z+.3z | | 1/5+1/2x=1/4x+5/6 | | -1/2=b/5 |

Equations solver categories