a^2=11a+18

Simple and best practice solution for a^2=11a+18 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 a^2=11a+18 equation:


Simplifying
a2 = 11a + 18

Reorder the terms:
a2 = 18 + 11a

Solving
a2 = 18 + 11a

Solving for variable 'a'.

Reorder the terms:
-18 + -11a + a2 = 18 + 11a + -18 + -11a

Reorder the terms:
-18 + -11a + a2 = 18 + -18 + 11a + -11a

Combine like terms: 18 + -18 = 0
-18 + -11a + a2 = 0 + 11a + -11a
-18 + -11a + a2 = 11a + -11a

Combine like terms: 11a + -11a = 0
-18 + -11a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -11a + 18 + a2 = 0 + 18

Reorder the terms:
-18 + 18 + -11a + a2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -11a + a2 = 0 + 18
-11a + a2 = 0 + 18

Combine like terms: 0 + 18 = 18
-11a + a2 = 18

The a term is -11a.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11a + 30.25 + a2 = 18 + 30.25

Reorder the terms:
30.25 + -11a + a2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + -11a + a2 = 48.25

Factor a perfect square on the left side:
(a + -5.5)(a + -5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(a + -5.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

a + -5.5 = 6.946221995 Simplifying a + -5.5 = 6.946221995 Reorder the terms: -5.5 + a = 6.946221995 Solving -5.5 + a = 6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = 6.946221995 + 5.5 a = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 a = 12.446221995 Simplifying a = 12.446221995

Subproblem 2

a + -5.5 = -6.946221995 Simplifying a + -5.5 = -6.946221995 Reorder the terms: -5.5 + a = -6.946221995 Solving -5.5 + a = -6.946221995 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + a = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + a = -6.946221995 + 5.5 a = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 a = -1.446221995 Simplifying a = -1.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. a = {12.446221995, -1.446221995}

See similar equations:

| 4y^2-8=y | | 0.3x-0.9=2.7 | | 2/3x=(3/2)-1 | | 8x+12x=67-7 | | (x-3)/8=4 | | x^2+8-108=0 | | 0=4-3(-4x-2) | | cos^2x+2cosx=3equation | | -45+6x=-2x+35 | | 2x+2(x-5)=30 | | 13s=2s+66 | | 9-6+14= | | X^3-6x^2+12x-224=0 | | x+4.9x-2=0 | | 7y^2+3y+1= | | 0.9x-0.5=9.4 | | X+9Y=200 | | 1/7x-3=11 | | 5000x=25000(60-x) | | 5x-5=45x+10 | | 756=450+0.5x(x+1) | | 8x-7y=20y | | -6+3y=1fory | | 19=(-2x)+3 | | -7x-5=6-8x | | 3(2x+6)-10x=45+5x | | 3-7t=-5t+4 | | (3x-2)-(x+1)=(2x+4)-(3x-2) | | 2x+31-x=8+5x-5 | | (2z+7)(3+z)=0 | | 27x=9(x-3) | | 2+2x=-1+3x |

Equations solver categories