a^2+3a-9=0

Simple and best practice solution for a^2+3a-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+3a-9=0 equation:


Simplifying
a2 + 3a + -9 = 0

Reorder the terms:
-9 + 3a + a2 = 0

Solving
-9 + 3a + 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 + 3a + 9 + a2 = 0 + 9

Reorder the terms:
-9 + 9 + 3a + a2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 3a + a2 = 0 + 9
3a + a2 = 0 + 9

Combine like terms: 0 + 9 = 9
3a + a2 = 9

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = 9 + 2.25

Reorder the terms:
2.25 + 3a + a2 = 9 + 2.25

Combine like terms: 9 + 2.25 = 11.25
2.25 + 3a + a2 = 11.25

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(a + 1.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

a + 1.5 = 3.354101966 Simplifying a + 1.5 = 3.354101966 Reorder the terms: 1.5 + a = 3.354101966 Solving 1.5 + a = 3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = 3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = 3.354101966 + -1.5 a = 3.354101966 + -1.5 Combine like terms: 3.354101966 + -1.5 = 1.854101966 a = 1.854101966 Simplifying a = 1.854101966

Subproblem 2

a + 1.5 = -3.354101966 Simplifying a + 1.5 = -3.354101966 Reorder the terms: 1.5 + a = -3.354101966 Solving 1.5 + a = -3.354101966 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + a = -3.354101966 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + a = -3.354101966 + -1.5 a = -3.354101966 + -1.5 Combine like terms: -3.354101966 + -1.5 = -4.854101966 a = -4.854101966 Simplifying a = -4.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.854101966, -4.854101966}

See similar equations:

| 2(2x+3)=(3x+8) | | j/5=1 | | 4x+3x-2x=2 | | 0.2*t^2+10.4=100 | | 6:3x=9 | | z=-36/12 | | a+(a+3)+(2a+b)=180 | | e=-120/-12 | | g=52/-4 | | f=-16/-4 | | 6a+4L=80 | | 36.18=.5(b+b)5.4 | | 36+(-28)+(-16)+24=y | | 7y-11y= | | x-3(2x-4x)=1+6x | | 5x-9=-7 | | 4(-5)(-6)=x | | 12(-5)=x | | -6(-5)(-6)=h | | -4(-6)(5)=x | | -19(-6)=y | | -8(-5)=x | | x^2+36+12x=0 | | -15(-5)=x | | 3(-6)=y | | (-3)(3)(-10)=t | | n=(16)(9)(-2) | | 3x^2+2xy+3y^2+2x=0 | | 1/2-5x=10 | | y=(20)(-5)(-5) | | 16t^2-12t-25=0 | | x+2:6=20 |

Equations solver categories