a^2+2a-9=0

Simple and best practice solution for a^2+2a-9=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+2a-9=0 equation:


Simplifying
a2 + 2a + -9 = 0

Reorder the terms:
-9 + 2a + a2 = 0

Solving
-9 + 2a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 2a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2a + a2 = 0 + 9
2a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
2a + a2 = 9

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 9 + 1

Reorder the terms:
1 + 2a + a2 = 9 + 1

Combine like terms: 9 + 1 = 10
1 + 2a + a2 = 10

Factor a perfect square on the left side:
(a + 1)(a + 1) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(a + 1) equal to 3.16227766 and -3.16227766.

Subproblem 1

a + 1 = 3.16227766 Simplifying a + 1 = 3.16227766 Reorder the terms: 1 + a = 3.16227766 Solving 1 + a = 3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + a = 3.16227766 + -1 a = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 a = 2.16227766 Simplifying a = 2.16227766

Subproblem 2

a + 1 = -3.16227766 Simplifying a + 1 = -3.16227766 Reorder the terms: 1 + a = -3.16227766 Solving 1 + a = -3.16227766 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + a = -3.16227766 + -1 a = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 a = -4.16227766 Simplifying a = -4.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. a = {2.16227766, -4.16227766}

See similar equations:

| 17/2x=17 | | -4/3x=32 | | -3/4x=-3 | | 3t^2-6t+7=0 | | 27+8x(37-17*2)= | | 32/8-2z/9=1 | | 1200=238/100 | | -3m+13-9(m-2)=7m-(5m-2)-6m+5 | | 2u=-2 | | -5p-2(2-6p)=2(p-5)-14 | | 8x^3-5x^2+5x-2=0 | | x=10x+6x | | -5p-2(-6p)=2(p-5)-14 | | -0.3t^2+24t=0 | | zy/x | | -9t=45 | | ((x^3)/(6b^3d^3))-((5du^3)/(2bc^2)) | | zy/x | | 6x-3x=1+11 | | 9x^2+113x+308=0 | | 6(x-5)4x=20 | | -9y=4 | | x+(x*0.095)=45 | | x+(x*1.095)=45 | | (5pq)q^2/35p^4q^8 | | 19/10 | | 15/35=x/100 | | 5x^2-46=0 | | -2b+4=3b-20 | | -4b+4+2b=3b-16-4 | | -y+3=14y | | 81x^2+18sqrt(1-x^2)-4=0 |

Equations solver categories