a(14a+5)=12

Simple and best practice solution for a(14a+5)=12 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(14a+5)=12 equation:


Simplifying
a(14a + 5) = 12

Reorder the terms:
a(5 + 14a) = 12
(5 * a + 14a * a) = 12
(5a + 14a2) = 12

Solving
5a + 14a2 = 12

Solving for variable 'a'.

Reorder the terms:
-12 + 5a + 14a2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 5a + 14a2 = 0

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

Divide each side by '14'.
-0.8571428571 + 0.3571428571a + a2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 0.3571428571a + 0.8571428571 + a2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 0.3571428571a + a2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 0.3571428571a + a2 = 0 + 0.8571428571
0.3571428571a + a2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
0.3571428571a + a2 = 0.8571428571

The a term is 0.3571428571a.  Take half its coefficient (0.1785714286).
Square it (0.03188775511) and add it to both sides.

Add '0.03188775511' to each side of the equation.
0.3571428571a + 0.03188775511 + a2 = 0.8571428571 + 0.03188775511

Reorder the terms:
0.03188775511 + 0.3571428571a + a2 = 0.8571428571 + 0.03188775511

Combine like terms: 0.8571428571 + 0.03188775511 = 0.88903061221
0.03188775511 + 0.3571428571a + a2 = 0.88903061221

Factor a perfect square on the left side:
(a + 0.1785714286)(a + 0.1785714286) = 0.88903061221

Calculate the square root of the right side: 0.942884199

Break this problem into two subproblems by setting 
(a + 0.1785714286) equal to 0.942884199 and -0.942884199.

Subproblem 1

a + 0.1785714286 = 0.942884199 Simplifying a + 0.1785714286 = 0.942884199 Reorder the terms: 0.1785714286 + a = 0.942884199 Solving 0.1785714286 + a = 0.942884199 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + a = 0.942884199 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + a = 0.942884199 + -0.1785714286 a = 0.942884199 + -0.1785714286 Combine like terms: 0.942884199 + -0.1785714286 = 0.7643127704 a = 0.7643127704 Simplifying a = 0.7643127704

Subproblem 2

a + 0.1785714286 = -0.942884199 Simplifying a + 0.1785714286 = -0.942884199 Reorder the terms: 0.1785714286 + a = -0.942884199 Solving 0.1785714286 + a = -0.942884199 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1785714286' to each side of the equation. 0.1785714286 + -0.1785714286 + a = -0.942884199 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + a = -0.942884199 + -0.1785714286 a = -0.942884199 + -0.1785714286 Combine like terms: -0.942884199 + -0.1785714286 = -1.1214556276 a = -1.1214556276 Simplifying a = -1.1214556276

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.7643127704, -1.1214556276}

See similar equations:

| (a+3)/b=c | | 5x^2-60+10=0 | | 7(-4x^3)= | | a+100b=21000 | | (3/4)x-4=16 | | 9y+20=164 | | 3y-9=15 | | (5/6)+5x=(2/3)-6x | | x+2=21-2x | | 3+4(x-9)=43 | | x+1-2x-2=-x | | X+1(x-3)=0 | | 15x^2+16x+3=0 | | 48x^3-336x^2-384x+6=0 | | -35-153= | | 6x-13x=56 | | 4x^2+4y^2+29x-51y=-196 | | 3(6x+6)-6x=3(4x+1)-6 | | 8-(-5x^3)= | | 12(3x+3)-6(2x-4)=4x-80 | | .24(24)+.04x=.12(18+x) | | b/7-1=-3 | | 4x+3y=1000 | | 2(-7)-(-5)= | | 38+(-18)+(-11)= | | 12+3v=30 | | 5u+7=32 | | 22-4t=10 | | 8(4a-4)=-5k-32 | | 12-(3m+6)=3+4m-18 | | 5+7(x-3)=75 | | (x/-3)=2 |

Equations solver categories