6a^2=19+7a

Simple and best practice solution for 6a^2=19+7a 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 6a^2=19+7a equation:


Simplifying
6a2 = 19 + 7a

Solving
6a2 = 19 + 7a

Solving for variable 'a'.

Reorder the terms:
-19 + -7a + 6a2 = 19 + 7a + -19 + -7a

Reorder the terms:
-19 + -7a + 6a2 = 19 + -19 + 7a + -7a

Combine like terms: 19 + -19 = 0
-19 + -7a + 6a2 = 0 + 7a + -7a
-19 + -7a + 6a2 = 7a + -7a

Combine like terms: 7a + -7a = 0
-19 + -7a + 6a2 = 0

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

Divide each side by '6'.
-3.166666667 + -1.166666667a + a2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + -1.166666667a + 3.166666667 + a2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + -1.166666667a + a2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + -1.166666667a + a2 = 0 + 3.166666667
-1.166666667a + a2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
-1.166666667a + a2 = 3.166666667

The a term is -1.166666667a.  Take half its coefficient (-0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
-1.166666667a + 0.3402777780 + a2 = 3.166666667 + 0.3402777780

Reorder the terms:
0.3402777780 + -1.166666667a + a2 = 3.166666667 + 0.3402777780

Combine like terms: 3.166666667 + 0.3402777780 = 3.506944445
0.3402777780 + -1.166666667a + a2 = 3.506944445

Factor a perfect square on the left side:
(a + -0.5833333335)(a + -0.5833333335) = 3.506944445

Calculate the square root of the right side: 1.872683755

Break this problem into two subproblems by setting 
(a + -0.5833333335) equal to 1.872683755 and -1.872683755.

Subproblem 1

a + -0.5833333335 = 1.872683755 Simplifying a + -0.5833333335 = 1.872683755 Reorder the terms: -0.5833333335 + a = 1.872683755 Solving -0.5833333335 + a = 1.872683755 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = 1.872683755 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = 1.872683755 + 0.5833333335 a = 1.872683755 + 0.5833333335 Combine like terms: 1.872683755 + 0.5833333335 = 2.4560170885 a = 2.4560170885 Simplifying a = 2.4560170885

Subproblem 2

a + -0.5833333335 = -1.872683755 Simplifying a + -0.5833333335 = -1.872683755 Reorder the terms: -0.5833333335 + a = -1.872683755 Solving -0.5833333335 + a = -1.872683755 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + a = -1.872683755 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + a = -1.872683755 + 0.5833333335 a = -1.872683755 + 0.5833333335 Combine like terms: -1.872683755 + 0.5833333335 = -1.2893504215 a = -1.2893504215 Simplifying a = -1.2893504215

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.4560170885, -1.2893504215}

See similar equations:

| 4p+12=14 | | -9+3x=9(1+x) | | -12(-10+4k)=8(3k+6) | | 8(n+7)+4(n-2)= | | 11x=48x | | -10x-20-12x-15=97 | | (3+4g)8=-8 | | x^3-2x^2-6=0 | | m^2=m+30 | | 6x-5x-7=3 | | (6x-5)=(3x+1) | | 5y+9=2y-6 | | 3(x^2+9)+3y^2=12 | | 2x^2-7m-3=0 | | 8(n+3)+4(n+3)= | | 5(x+9)+6=11 | | 21n^2+13n-30=0 | | 4(x+5)-6=3+3x | | -4(T-2)+9T=3T-2 | | 7a^2+50a+48=0 | | x-8+2x=16-5x | | 3/5(2x+3)=8 | | 3(x-4)=x+4 | | 4-5(2x+6)=9x+(-7) | | -5z-2z=8z+5+8z | | 4(2x-3x)=20 | | x^2-3m-10=0 | | 27=7x | | -7x^2+33x+10=0 | | 2x-8=3x+(-9) | | 6x-60+8x+96=92 | | 45=3p+18 |

Equations solver categories