a^2+4a+4=45

Simple and best practice solution for a^2+4a+4=45 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+4a+4=45 equation:


Simplifying
a2 + 4a + 4 = 45

Reorder the terms:
4 + 4a + a2 = 45

Solving
4 + 4a + a2 = 45

Solving for variable 'a'.

Reorder the terms:
4 + -45 + 4a + a2 = 45 + -45

Combine like terms: 4 + -45 = -41
-41 + 4a + a2 = 45 + -45

Combine like terms: 45 + -45 = 0
-41 + 4a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 4a + 41 + a2 = 0 + 41

Reorder the terms:
-41 + 41 + 4a + a2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 4a + a2 = 0 + 41
4a + a2 = 0 + 41

Combine like terms: 0 + 41 = 41
4a + a2 = 41

The a term is 4a.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4a + 4 + a2 = 41 + 4

Reorder the terms:
4 + 4a + a2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + 4a + a2 = 45

Factor a perfect square on the left side:
(a + 2)(a + 2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(a + 2) equal to 6.708203933 and -6.708203933.

Subproblem 1

a + 2 = 6.708203933 Simplifying a + 2 = 6.708203933 Reorder the terms: 2 + a = 6.708203933 Solving 2 + a = 6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + a = 6.708203933 + -2 a = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 a = 4.708203933 Simplifying a = 4.708203933

Subproblem 2

a + 2 = -6.708203933 Simplifying a + 2 = -6.708203933 Reorder the terms: 2 + a = -6.708203933 Solving 2 + a = -6.708203933 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + a = -6.708203933 + -2 a = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 a = -8.708203933 Simplifying a = -8.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. a = {4.708203933, -8.708203933}

See similar equations:

| 9m-22=4m | | 4(2p-3)=5 | | 4(2p-3)=4 | | 0=-16t^2+16t+200 | | 4X+2Y=-30 | | p+12.3=-6.1 | | 4(2x-3)=5 | | -3x(x-1)=5-(X+1) | | 576+r^2=256+r^2 | | 200=-16t^2+16t+480 | | 7(c+25)=2(c+20) | | 6w-12=42 | | (4x-1)(6x+5)-(8x-1)(3x+5)=-23x | | 2(v+12)=64 | | 12x+36=0 | | 2y+4=8y-16 | | 5(2x-1)=65 | | 3+3g=15 | | 3m+5=7m-3 | | 7x^2=1024 | | 5(x+4x-25)=50 | | 6e+5f=e-3f | | 3.8(-6)+4.6=-22 | | x-23-10+25=42 | | 7(v+4)=98 | | 5x^2-3-6=0 | | 18+18+20+20+x=99 | | 120-43x+x^2=0 | | 1.75+2(2-g)=0 | | 6-x=13-2 | | 7x-8=2x+2 | | x+9.75+4.50=62.65 |

Equations solver categories