2L^2-50L+150=0

Simple and best practice solution for 2L^2-50L+150=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 2L^2-50L+150=0 equation: 


Simplifying
2L2 + -50L + 150 = 0

Reorder the terms:
150 + -50L + 2L2 = 0

Solving
150 + -50L + 2L2 = 0

Solving for variable 'L'.

Factor out the Greatest Common Factor (GCF), '2'.
2(75 + -25L + L2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(75 + -25L + L2)' equal to zero and attempt to solve:

Simplifying
75 + -25L + L2 = 0

Solving
75 + -25L + L2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -25L + -75 + L2 = 0 + -75

Reorder the terms:
75 + -75 + -25L + L2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -25L + L2 = 0 + -75
-25L + L2 = 0 + -75

Combine like terms: 0 + -75 = -75
-25L + L2 = -75

The L term is -25L.  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.
-25L + 156.25 + L2 = -75 + 156.25

Reorder the terms:
156.25 + -25L + L2 = -75 + 156.25

Combine like terms: -75 + 156.25 = 81.25
156.25 + -25L + L2 = 81.25

Factor a perfect square on the left side:
(L + -12.5)(L + -12.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(L + -12.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
L + -12.5 = 9.013878189

Simplifying
L + -12.5 = 9.013878189

Reorder the terms:
-12.5 + L = 9.013878189

Solving
-12.5 + L = 9.013878189

Solving for variable 'L'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + L = 9.013878189 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + L = 9.013878189 + 12.5
L = 9.013878189 + 12.5

Combine like terms: 9.013878189 + 12.5 = 21.513878189
L = 21.513878189

Simplifying
L = 21.513878189


Subproblem 2
L + -12.5 = -9.013878189

Simplifying
L + -12.5 = -9.013878189

Reorder the terms:
-12.5 + L = -9.013878189

Solving
-12.5 + L = -9.013878189

Solving for variable 'L'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + L = -9.013878189 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + L = -9.013878189 + 12.5
L = -9.013878189 + 12.5

Combine like terms: -9.013878189 + 12.5 = 3.486121811
L = 3.486121811

Simplifying
L = 3.486121811


Solution
The solution to the problem is based on the solutions
from the subproblems.
L = {21.513878189, 3.486121811}
Solution
L = {21.513878189, 3.486121811}

See similar equations:

| 6k-3k=9 | | 3m^2-15m-1=0 | | 6-x/4=-8 | | 6x+2=x-1 | | 2x-8=-6x+8/2 | | -4a*2a*1-5a-6a=10-10a | | 2x+1o=-2 | | (4x^2-10x-24)/(2x+3) | | 3x+5=y+3 | | 2v*3v^2y^3*8y^9= | | -5x+2x=-8-10 | | (3x^2-11)(3x^2+11)= | | x^2/4=2x-10 | | 8x-4=6-10 | | 25/16*a^4*b^2*c^8 | | 4(2d-9)= | | (8x+3)(4x+7)= | | 0.3x+0.4=0.2x | | 8y-47y=7 | | 3+9=7t-9 | | x+43=-18 | | 8x^2-4xy-4y= | | 6n^2-63=-3n | | 21w^5-4w^5= | | x=48.8-.08x | | -3z^4-11z^4= | | 2+12=5t-6 | | x=243+0.4x | | 70+25a=200 | | 15m+4=23m | | 8=-9h+26 | | x^2-4.7x=-28 |

Equations solver categories