L^2-23L=90

Simple and best practice solution for L^2-23L=90 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 L^2-23L=90 equation:


Simplifying
L2 + -23L = 90

Reorder the terms:
-23L + L2 = 90

Solving
-23L + L2 = 90

Solving for variable 'L'.

Reorder the terms:
-90 + -23L + L2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -23L + L2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -23L + 90 + L2 = 0 + 90

Reorder the terms:
-90 + 90 + -23L + L2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -23L + L2 = 0 + 90
-23L + L2 = 0 + 90

Combine like terms: 0 + 90 = 90
-23L + L2 = 90

The L term is -23L.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23L + 132.25 + L2 = 90 + 132.25

Reorder the terms:
132.25 + -23L + L2 = 90 + 132.25

Combine like terms: 90 + 132.25 = 222.25
132.25 + -23L + L2 = 222.25

Factor a perfect square on the left side:
(L + -11.5)(L + -11.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(L + -11.5) equal to 14.908051516 and -14.908051516.

Subproblem 1

L + -11.5 = 14.908051516 Simplifying L + -11.5 = 14.908051516 Reorder the terms: -11.5 + L = 14.908051516 Solving -11.5 + L = 14.908051516 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + L = 14.908051516 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + L = 14.908051516 + 11.5 L = 14.908051516 + 11.5 Combine like terms: 14.908051516 + 11.5 = 26.408051516 L = 26.408051516 Simplifying L = 26.408051516

Subproblem 2

L + -11.5 = -14.908051516 Simplifying L + -11.5 = -14.908051516 Reorder the terms: -11.5 + L = -14.908051516 Solving -11.5 + L = -14.908051516 Solving for variable 'L'. Move all terms containing L to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + L = -14.908051516 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + L = -14.908051516 + 11.5 L = -14.908051516 + 11.5 Combine like terms: -14.908051516 + 11.5 = -3.408051516 L = -3.408051516 Simplifying L = -3.408051516

Solution

The solution to the problem is based on the solutions from the subproblems. L = {26.408051516, -3.408051516}

See similar equations:

| (x^2-y^3)(x^2+y^3)(x^4+y^6)= | | 0.9a=0.6a | | 3x-18=36 | | 2x-4=3x+1 | | 6=2a+11 | | -3(x-1)+8(x-3)=6x+7-5 | | 8(3-x)=-2(x+5) | | -2(n-5)-(3n-5)=-6n | | -9(v+3)+2v+7=8v+6 | | x(3x^2-23)=8 | | 4(x-3)(x+3)(x^2+9)= | | 4w^6+24w^5+36w^4= | | 3v+-v=-4 | | 2a=2a-11 | | 4x^3+4x^2-9x-9=0 | | 2m^2-15m+13=0 | | 2m^2-15m+13=0 | | 2(3x-8)=5(2-x) | | (2x^2-19x+24)=0 | | 2(2x^2-19x+24)=0 | | 3w^2+7w+2=0 | | (d+3)4=(d+12)3 | | -8(v+4)+3v+6=8v+7 | | 9-2[6-(9y-2)]= | | u^4+8u^3+20u^2= | | 13-9x=5-x | | 2(2x^2-19+24)=0 | | 2w^2+3w=54 | | 9-(2x-5)=3-3x | | (9x-11)(9x-11)=99 | | 1-y/3=6 | | 2x^2-19+24=0 |

Equations solver categories