10x^2-42x+4=0

Simple and best practice solution for 10x^2-42x+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 10x^2-42x+4=0 equation: 


Simplifying
10x2 + -42x + 4 = 0

Reorder the terms:
4 + -42x + 10x2 = 0

Solving
4 + -42x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -21x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -21x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + -21x + 5x2 = 0

Solving
2 + -21x + 5x2 = 0

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

Divide each side by '5'.
0.4 + -4.2x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -4.2x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -4.2x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -4.2x + x2 = 0 + -0.4
-4.2x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-4.2x + x2 = -0.4

The x term is -4.2x.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2x + 4.41 + x2 = -0.4 + 4.41

Reorder the terms:
4.41 + -4.2x + x2 = -0.4 + 4.41

Combine like terms: -0.4 + 4.41 = 4.01
4.41 + -4.2x + x2 = 4.01

Factor a perfect square on the left side:
(x + -2.1)(x + -2.1) = 4.01

Calculate the square root of the right side: 2.002498439

Break this problem into two subproblems by setting 
(x + -2.1) equal to 2.002498439 and -2.002498439.


Subproblem 1
x + -2.1 = 2.002498439

Simplifying
x + -2.1 = 2.002498439

Reorder the terms:
-2.1 + x = 2.002498439

Solving
-2.1 + x = 2.002498439

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = 2.002498439 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = 2.002498439 + 2.1
x = 2.002498439 + 2.1

Combine like terms: 2.002498439 + 2.1 = 4.102498439
x = 4.102498439

Simplifying
x = 4.102498439


Subproblem 2
x + -2.1 = -2.002498439

Simplifying
x + -2.1 = -2.002498439

Reorder the terms:
-2.1 + x = -2.002498439

Solving
-2.1 + x = -2.002498439

Solving for variable 'x'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + x = -2.002498439 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + x = -2.002498439 + 2.1
x = -2.002498439 + 2.1

Combine like terms: -2.002498439 + 2.1 = 0.097501561
x = 0.097501561

Simplifying
x = 0.097501561


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.102498439, 0.097501561}
Solution
x = {4.102498439, 0.097501561}

See similar equations:

| 8+3.5r=r | | cos(11x)=0 | | f(x)=3x^2-6x+5 | | 5(t-2)+3(t-13)=23 | | 16x+6(x-2)= | | 246+m+m+7m=3m+354 | | 52x=89 | | x^2-10y^2=-1 | | 3(4y+18)-11y=50 | | 32+1x=12+11x | | (x)=-0.04x^2+240x-10000 | | x^2+7x+15=x+6 | | -7-5a=28 | | 27y^2-35y+8=0 | | x=4(104)+18 | | (5x-16)=2x | | 6-4x=6x-8x+3 | | 3(4y-18)-11y=50 | | (4x-7)(8x+5)=0 | | (8x-2)(3x+4)=(4x+3)(6x+1) | | 11x^3+18x^2+9x=0 | | 5x^2+16-3=5-2x | | x^2+x=x+4 | | 5.5x+0.65=-1.64 | | -2[b-3]+8= | | a^2+12a= | | x^2+x+7=6x+3 | | (-3)2*(5-7)2-(-9)/3=39 | | -5x+9=-9.8 | | 360x^2-12x-2550=0 | | 28.8+10b=15b+3.8 | | (-3)2*(5-7)2-(-9)/3= |

Equations solver categories