4x^2-30x+10=0

Simple and best practice solution for 4x^2-30x+10=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+10=0 equation: 


Simplifying
4x2 + -30x + 10 = 0

Reorder the terms:
10 + -30x + 4x2 = 0

Solving
10 + -30x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -15x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + -15x + 2x2 = 0

Solving
5 + -15x + 2x2 = 0

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

Divide each side by '2'.
2.5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -7.5x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -7.5x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -7.5x + x2 = 0 + -2.5
-7.5x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-7.5x + x2 = -2.5

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 = -2.5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -2.5 + 14.0625

Combine like terms: -2.5 + 14.0625 = 11.5625
14.0625 + -7.5x + x2 = 11.5625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.400367627 and -3.400367627.


Subproblem 1
x + -3.75 = 3.400367627

Simplifying
x + -3.75 = 3.400367627

Reorder the terms:
-3.75 + x = 3.400367627

Solving
-3.75 + x = 3.400367627

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 = 3.400367627 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.400367627 + 3.75
x = 3.400367627 + 3.75

Combine like terms: 3.400367627 + 3.75 = 7.150367627
x = 7.150367627

Simplifying
x = 7.150367627


Subproblem 2
x + -3.75 = -3.400367627

Simplifying
x + -3.75 = -3.400367627

Reorder the terms:
-3.75 + x = -3.400367627

Solving
-3.75 + x = -3.400367627

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 = -3.400367627 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.400367627 + 3.75
x = -3.400367627 + 3.75

Combine like terms: -3.400367627 + 3.75 = 0.349632373
x = 0.349632373

Simplifying
x = 0.349632373


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.150367627, 0.349632373}
Solution
x = {7.150367627, 0.349632373}

See similar equations:

| -5x-2(7x-17)=80 | | 12+5x=7(x-2) | | 8p-5=19 | | .5t+36=15 | | x^2+4x-100000000=0 | | 30-(30-2h)=2h | | 40x+20=50y | | 6x+y-4=180 | | -5(3z+5)= | | Y=121x^2-49 | | e^2x-7=987 | | (1/4)(4/17) | | -4(x+2)-42=1-23 | | 8x+18-7x=-4-12 | | 14x=14-(-14) | | 14x=14-(14) | | 483*14= | | -7(x+3)-17=10+8 | | 3^6z^-4/3^7z^-8= | | 13(x-9)=-6-7 | | 121/164 | | 6X^2+30X=900 | | x+kx+1=0 | | 2x+(2x+2)+(2x+4)=102 | | z^10+1=2i | | kx^2-x-(k-2)=0 | | ln(x-1)-ln(x+3)=ln(11) | | -5lnx=1 | | 9y^2-16x^2-18y+9=0 | | 4-3x=2x^2 | | 5/6×t-7 | | -3=3m^2-2m+6 |

Equations solver categories