6x^2-150x+400=0

Simple and best practice solution for 6x^2-150x+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 6x^2-150x+400=0 equation: 


Simplifying
6x2 + -150x + 400 = 0

Reorder the terms:
400 + -150x + 6x2 = 0

Solving
400 + -150x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(200 + -75x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(200 + -75x + 3x2)' equal to zero and attempt to solve:

Simplifying
200 + -75x + 3x2 = 0

Solving
200 + -75x + 3x2 = 0

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

Divide each side by '3'.
66.66666667 + -25x + x2 = 0

Move the constant term to the right:

Add '-66.66666667' to each side of the equation.
66.66666667 + -25x + -66.66666667 + x2 = 0 + -66.66666667

Reorder the terms:
66.66666667 + -66.66666667 + -25x + x2 = 0 + -66.66666667

Combine like terms: 66.66666667 + -66.66666667 = 0.00000000
0.00000000 + -25x + x2 = 0 + -66.66666667
-25x + x2 = 0 + -66.66666667

Combine like terms: 0 + -66.66666667 = -66.66666667
-25x + x2 = -66.66666667

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -66.66666667 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -66.66666667 + 156.25

Combine like terms: -66.66666667 + 156.25 = 89.58333333
156.25 + -25x + x2 = 89.58333333

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 89.58333333

Calculate the square root of the right side: 9.464847243

Break this problem into two subproblems by setting 
(x + -12.5) equal to 9.464847243 and -9.464847243.


Subproblem 1
x + -12.5 = 9.464847243

Simplifying
x + -12.5 = 9.464847243

Reorder the terms:
-12.5 + x = 9.464847243

Solving
-12.5 + x = 9.464847243

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = 9.464847243 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = 9.464847243 + 12.5
x = 9.464847243 + 12.5

Combine like terms: 9.464847243 + 12.5 = 21.964847243
x = 21.964847243

Simplifying
x = 21.964847243


Subproblem 2
x + -12.5 = -9.464847243

Simplifying
x + -12.5 = -9.464847243

Reorder the terms:
-12.5 + x = -9.464847243

Solving
-12.5 + x = -9.464847243

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x = -9.464847243 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x = -9.464847243 + 12.5
x = -9.464847243 + 12.5

Combine like terms: -9.464847243 + 12.5 = 3.035152757
x = 3.035152757

Simplifying
x = 3.035152757


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.964847243, 3.035152757}
Solution
x = {21.964847243, 3.035152757}

See similar equations:

| 102=-3(8x+6) | | 8x-39=11x | | 0.4y=1.6 | | 0.003=x/0.012 | | 5,432/100k=50 | | -(-1-5x)+2(5x-8)=30 | | (n+1)(n)(n+1)=210 | | 8+2*10= | | 3x/5=5/6 | | 3x/5=-5/6 | | 81(x-1)(x-1)=4 | | 81x^2-162x-81=4 | | 18e=-42 | | 0.2=x/1 | | 2x+155=11x-7 | | 2x-6=6x^2 | | ax+4=bx+7-12y | | 4qr+8r-6q=12 | | 350/400 | | x^4-11x^3+29x^2+11x-30=0 | | x^44-11x^3+29x^2+11x-30=0 | | 4x^2-17y+18=0 | | sinx=-cosy | | 5y-3=3y-7 | | 36+-2x=4x | | x^2+x^2-5x+6=0 | | 70=8*w*3 | | x^2+3=2x+6 | | Ab+ma=a(b+m) | | 2a+4=2(a+2) | | x=(0.65*x)+9 | | 100,000*1/3 |

Equations solver categories