a(2a+3)-18=0

Simple and best practice solution for a(2a+3)-18=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 a(2a+3)-18=0 equation:


Simplifying
a(2a + 3) + -18 = 0

Reorder the terms:
a(3 + 2a) + -18 = 0
(3 * a + 2a * a) + -18 = 0
(3a + 2a2) + -18 = 0

Reorder the terms:
-18 + 3a + 2a2 = 0

Solving
-18 + 3a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
-9 + 1.5a + a2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 1.5a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 1.5a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 1.5a + a2 = 0 + 9
1.5a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
1.5a + a2 = 9

The a term is 1.5a.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5a + 0.5625 + a2 = 9 + 0.5625

Reorder the terms:
0.5625 + 1.5a + a2 = 9 + 0.5625

Combine like terms: 9 + 0.5625 = 9.5625
0.5625 + 1.5a + a2 = 9.5625

Factor a perfect square on the left side:
(a + 0.75)(a + 0.75) = 9.5625

Calculate the square root of the right side: 3.092329219

Break this problem into two subproblems by setting 
(a + 0.75) equal to 3.092329219 and -3.092329219.

Subproblem 1

a + 0.75 = 3.092329219 Simplifying a + 0.75 = 3.092329219 Reorder the terms: 0.75 + a = 3.092329219 Solving 0.75 + a = 3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = 3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = 3.092329219 + -0.75 a = 3.092329219 + -0.75 Combine like terms: 3.092329219 + -0.75 = 2.342329219 a = 2.342329219 Simplifying a = 2.342329219

Subproblem 2

a + 0.75 = -3.092329219 Simplifying a + 0.75 = -3.092329219 Reorder the terms: 0.75 + a = -3.092329219 Solving 0.75 + a = -3.092329219 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + a = -3.092329219 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + a = -3.092329219 + -0.75 a = -3.092329219 + -0.75 Combine like terms: -3.092329219 + -0.75 = -3.842329219 a = -3.842329219 Simplifying a = -3.842329219

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.342329219, -3.842329219}

See similar equations:

| 2b+4a+2a=180 | | 18x^2-6x=0 | | m^2-5=-4m | | 8x-(6x+4)=6 | | -42=-5x+24-(5x+11) | | 11x-32=6x-7 | | m^2-5=4m | | 3(7x-3)=25 | | -5x+3(2x-11)=-13 | | 8(2x-4)-8x=-32 | | 159-6x=4x+9 | | -4-(d+11)-6d=34 | | 5+3=8 | | 6x+4x-x+5=23 | | 10.5=-9.4 | | 10=-4(x-4)-10x+22 | | 9x-7+6x=53 | | 3x+4x-3=25 | | 1x-4=10 | | 9x+10=-6x-3 | | 7x+1=3x+1 | | y=x^4+15x^2-16 | | 7x+76.4=6x-2 | | -564x+10=11.77x-638.2 | | w^2=18-7w | | 3x-98.21=66.45x | | 5-3*-5-8= | | 5-3*(-5)-8= | | 6x-(3x+8)=16 | | 9=3(5x-2) | | 0.2+0.9=0.3-0.1x | | 5+4x-7=4x-2-x |

Equations solver categories