a^2+10a+6=0

Simple and best practice solution for a^2+10a+6=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+10a+6=0 equation:


Simplifying
a2 + 10a + 6 = 0

Reorder the terms:
6 + 10a + a2 = 0

Solving
6 + 10a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 10a + -6 + a2 = 0 + -6

Reorder the terms:
6 + -6 + 10a + a2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 10a + a2 = 0 + -6
10a + a2 = 0 + -6

Combine like terms: 0 + -6 = -6
10a + a2 = -6

The a term is 10a.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10a + 25 + a2 = -6 + 25

Reorder the terms:
25 + 10a + a2 = -6 + 25

Combine like terms: -6 + 25 = 19
25 + 10a + a2 = 19

Factor a perfect square on the left side:
(a + 5)(a + 5) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(a + 5) equal to 4.358898944 and -4.358898944.

Subproblem 1

a + 5 = 4.358898944 Simplifying a + 5 = 4.358898944 Reorder the terms: 5 + a = 4.358898944 Solving 5 + a = 4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = 4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + a = 4.358898944 + -5 a = 4.358898944 + -5 Combine like terms: 4.358898944 + -5 = -0.641101056 a = -0.641101056 Simplifying a = -0.641101056

Subproblem 2

a + 5 = -4.358898944 Simplifying a + 5 = -4.358898944 Reorder the terms: 5 + a = -4.358898944 Solving 5 + a = -4.358898944 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + a = -4.358898944 + -5 Combine like terms: 5 + -5 = 0 0 + a = -4.358898944 + -5 a = -4.358898944 + -5 Combine like terms: -4.358898944 + -5 = -9.358898944 a = -9.358898944 Simplifying a = -9.358898944

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.641101056, -9.358898944}

See similar equations:

| 30=t/5-10 | | 118-6x=39x+23 | | .05(6-m)-2.4(2)=-0.35m | | 7/8(32+16x)=-7-14 | | 5-9x=31-16x | | 8x-66=69-x | | x-1/2-x-3/4=6-x-3/5 | | y^2+12y-64=0 | | x/3-3/4=5x/12+1 | | 43-4x=5x+17 | | 8/m-5+21/m=0 | | 4x-8-6-4x=5x+1 | | -83+x=79-5x | | 10-9x=47-16x | | 3(5x-1)+15=11x-4 | | 6x+209=16x-11 | | y+5/y | | (10-3)*8=m | | y+5/y=10/8 | | 10-3*8=m | | 6/(2x-1)=2 | | (2x-30)+x+3x=180 | | 6x+5=-43 | | 7x+13=9x+1 | | 3(x-4)-x=3x-(4+2x) | | 7+5n=8n+1 | | y^2+12y-32=32 | | -3t^2+114t+117=0 | | x^2-2x=180 | | 2x+(2/3x+5)+(11-x) | | X^2+10+7x=0 | | x=10-y |

Equations solver categories