a^2+13a-68=52

Simple and best practice solution for a^2+13a-68=52 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+13a-68=52 equation:


Simplifying
a2 + 13a + -68 = 52

Reorder the terms:
-68 + 13a + a2 = 52

Solving
-68 + 13a + a2 = 52

Solving for variable 'a'.

Reorder the terms:
-68 + -52 + 13a + a2 = 52 + -52

Combine like terms: -68 + -52 = -120
-120 + 13a + a2 = 52 + -52

Combine like terms: 52 + -52 = 0
-120 + 13a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 13a + 120 + a2 = 0 + 120

Reorder the terms:
-120 + 120 + 13a + a2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 13a + a2 = 0 + 120
13a + a2 = 0 + 120

Combine like terms: 0 + 120 = 120
13a + a2 = 120

The a term is 13a.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13a + 42.25 + a2 = 120 + 42.25

Reorder the terms:
42.25 + 13a + a2 = 120 + 42.25

Combine like terms: 120 + 42.25 = 162.25
42.25 + 13a + a2 = 162.25

Factor a perfect square on the left side:
(a + 6.5)(a + 6.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(a + 6.5) equal to 12.737739203 and -12.737739203.

Subproblem 1

a + 6.5 = 12.737739203 Simplifying a + 6.5 = 12.737739203 Reorder the terms: 6.5 + a = 12.737739203 Solving 6.5 + a = 12.737739203 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 12.737739203 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 12.737739203 + -6.5 a = 12.737739203 + -6.5 Combine like terms: 12.737739203 + -6.5 = 6.237739203 a = 6.237739203 Simplifying a = 6.237739203

Subproblem 2

a + 6.5 = -12.737739203 Simplifying a + 6.5 = -12.737739203 Reorder the terms: 6.5 + a = -12.737739203 Solving 6.5 + a = -12.737739203 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -12.737739203 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -12.737739203 + -6.5 a = -12.737739203 + -6.5 Combine like terms: -12.737739203 + -6.5 = -19.237739203 a = -19.237739203 Simplifying a = -19.237739203

Solution

The solution to the problem is based on the solutions from the subproblems. a = {6.237739203, -19.237739203}

See similar equations:

| 2a/5=18/15 | | 5b^2-10b^3+25b^4= | | 8x-12x-4x-5x=9+13 | | a^2+13a-68= | | 8x+12x-4x-5x=9+13 | | -5(4t-5)+6t=3t-2 | | 4p+2m=8 | | 3xy-3xz= | | M-3.87=7.49 | | h+89.4=97.4 | | 2a*15=18*15 | | x+(26-x)=26 | | 54/6=81/b | | 4m-21+5m=51 | | a^25=1.4 | | 100+c=129 | | 3(2x+3)=5x+5 | | 16x^2-12x+24= | | x+(x-26)=26 | | x+8=-x+1 | | 17t-t=54 | | 47=17+v | | 7-8n=4+3n | | 5=w+16 | | 8+f=20 | | 11/14+1/10 | | x^5-x^3-x= | | 15=-8(b-1)9 | | 28.8/3 | | -4s-12=s/5 | | -4(y-2)= | | 921x+200770=2419x+183106 |

Equations solver categories