4x^2-30x+4=0

Simple and best practice solution for 4x^2-30x+4=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^2-30x+4=0 equation: 


Simplifying
4x2 + -30x + 4 = 0

Reorder the terms:
4 + -30x + 4x2 = 0

Solving
4 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -15x + 2x2 = 0

Solving
2 + -15x + 2x2 = 0

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

Divide each side by '2'.
1 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -7.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7.5x + x2 = 0 + -1
-7.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7.5x + x2 = -1

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -1 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -1 + 14.0625

Combine like terms: -1 + 14.0625 = 13.0625
14.0625 + -7.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.614208074 and -3.614208074.


Subproblem 1
x + -3.75 = 3.614208074

Simplifying
x + -3.75 = 3.614208074

Reorder the terms:
-3.75 + x = 3.614208074

Solving
-3.75 + x = 3.614208074

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.614208074 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.614208074 + 3.75
x = 3.614208074 + 3.75

Combine like terms: 3.614208074 + 3.75 = 7.364208074
x = 7.364208074

Simplifying
x = 7.364208074


Subproblem 2
x + -3.75 = -3.614208074

Simplifying
x + -3.75 = -3.614208074

Reorder the terms:
-3.75 + x = -3.614208074

Solving
-3.75 + x = -3.614208074

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.614208074 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.614208074 + 3.75
x = -3.614208074 + 3.75

Combine like terms: -3.614208074 + 3.75 = 0.135791926
x = 0.135791926

Simplifying
x = 0.135791926


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.364208074, 0.135791926}
Solution
x = {7.364208074, 0.135791926}

See similar equations:

| 20+14t+2t^2=0 | | x-176=3x | | y=8(20) | | Y=-2x^2-8x-20 | | Y=2x^2-8x-20 | | -52=4(-4-3x)+3x | | 2(4x-2)-x=-18 | | 2x^2y+6xy-58y=0 | | 9t+4=t+36 | | 3x^3+30x^2+27x=0 | | .9=a+3b | | a+2b+4c=100 | | (3+2i)+(4+7i)=7-5i | | a+b^2+c^4=100 | | a+b^2+c^4= | | -3=-4+x | | (6x+6)+(9x+7)= | | 5(t-8)-3(2t-5)=4-8(3t+5) | | 9x^2+9=7x^2+27 | | 2y=(9-3x) | | 89=4u+13 | | -8a-1=-28 | | 35=5y-15 | | Y=x^4+x^2-30 | | x-9.9=43 | | -19n+10n+15-n=-5 | | 8(3a+6)+a-12= | | 3z-5=25 | | 2x+60+6x=180 | | 3-5=25 | | 0.5(7d+4)=7-1.5d | | 110=20y |

Equations solver categories