a^2-6a-51=0

Simple and best practice solution for a^2-6a-51=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^2-6a-51=0 equation:


Simplifying
a2 + -6a + -51 = 0

Reorder the terms:
-51 + -6a + a2 = 0

Solving
-51 + -6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -6a + 51 + a2 = 0 + 51

Reorder the terms:
-51 + 51 + -6a + a2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -6a + a2 = 0 + 51
-6a + a2 = 0 + 51

Combine like terms: 0 + 51 = 51
-6a + a2 = 51

The a term is -6a.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6a + 9 + a2 = 51 + 9

Reorder the terms:
9 + -6a + a2 = 51 + 9

Combine like terms: 51 + 9 = 60
9 + -6a + a2 = 60

Factor a perfect square on the left side:
(a + -3)(a + -3) = 60

Calculate the square root of the right side: 7.745966692

Break this problem into two subproblems by setting 
(a + -3) equal to 7.745966692 and -7.745966692.

Subproblem 1

a + -3 = 7.745966692 Simplifying a + -3 = 7.745966692 Reorder the terms: -3 + a = 7.745966692 Solving -3 + a = 7.745966692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = 7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + a = 7.745966692 + 3 a = 7.745966692 + 3 Combine like terms: 7.745966692 + 3 = 10.745966692 a = 10.745966692 Simplifying a = 10.745966692

Subproblem 2

a + -3 = -7.745966692 Simplifying a + -3 = -7.745966692 Reorder the terms: -3 + a = -7.745966692 Solving -3 + a = -7.745966692 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + a = -7.745966692 + 3 Combine like terms: -3 + 3 = 0 0 + a = -7.745966692 + 3 a = -7.745966692 + 3 Combine like terms: -7.745966692 + 3 = -4.745966692 a = -4.745966692 Simplifying a = -4.745966692

Solution

The solution to the problem is based on the solutions from the subproblems. a = {10.745966692, -4.745966692}

See similar equations:

| 0=-48+6x | | 0=4t-84 | | 0.96x^2-2x+0.96=0 | | 5x-15+20=30 | | 0=7t-49 | | (x-3)squared=49 | | 42x+6=20 | | 9j=-3/5 | | 12-s=19-2s | | 7y+3=3y+27 | | x^4-8x^3-x+8=0 | | Log(7)+log(-x)=log(6-x) | | Log(x^2+x)=40 | | 3*sinx*cosx=1 | | 0.07*28kg= | | y=5/3(1)-1 | | 7-2x=5x+3 | | 4n+3=2n+17 | | x/3/10=15 | | ln(x+4)=ln(18) | | x+4(x-1)=5-2(x+3) | | f(x+4)=x^2+2x+9 | | 10x/18x | | 13y-14=9y+10 | | 20x-4y=40 | | 20-4y=40 | | Z^2-Z+5-3i=0 | | 38s+15=-25 | | 2w+3.5=2.1+w | | 10y=4y+10-5y | | m+13=2m+5 | | r^2=48-2 |

Equations solver categories