x^2+78x+243=0

Simple and best practice solution for x^2+78x+243=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 x^2+78x+243=0 equation:


Simplifying
x2 + 78x + 243 = 0

Reorder the terms:
243 + 78x + x2 = 0

Solving
243 + 78x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-243' to each side of the equation.
243 + 78x + -243 + x2 = 0 + -243

Reorder the terms:
243 + -243 + 78x + x2 = 0 + -243

Combine like terms: 243 + -243 = 0
0 + 78x + x2 = 0 + -243
78x + x2 = 0 + -243

Combine like terms: 0 + -243 = -243
78x + x2 = -243

The x term is 78x.  Take half its coefficient (39).
Square it (1521) and add it to both sides.

Add '1521' to each side of the equation.
78x + 1521 + x2 = -243 + 1521

Reorder the terms:
1521 + 78x + x2 = -243 + 1521

Combine like terms: -243 + 1521 = 1278
1521 + 78x + x2 = 1278

Factor a perfect square on the left side:
(x + 39)(x + 39) = 1278

Calculate the square root of the right side: 35.749125863

Break this problem into two subproblems by setting 
(x + 39) equal to 35.749125863 and -35.749125863.

Subproblem 1

x + 39 = 35.749125863 Simplifying x + 39 = 35.749125863 Reorder the terms: 39 + x = 35.749125863 Solving 39 + x = 35.749125863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = 35.749125863 + -39 Combine like terms: 39 + -39 = 0 0 + x = 35.749125863 + -39 x = 35.749125863 + -39 Combine like terms: 35.749125863 + -39 = -3.250874137 x = -3.250874137 Simplifying x = -3.250874137

Subproblem 2

x + 39 = -35.749125863 Simplifying x + 39 = -35.749125863 Reorder the terms: 39 + x = -35.749125863 Solving 39 + x = -35.749125863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = -35.749125863 + -39 Combine like terms: 39 + -39 = 0 0 + x = -35.749125863 + -39 x = -35.749125863 + -39 Combine like terms: -35.749125863 + -39 = -74.749125863 x = -74.749125863 Simplifying x = -74.749125863

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.250874137, -74.749125863}

See similar equations:

| (x+8)(x+8)=0 | | r^2-3r+1=0 | | -6(x-1)=-6x-56 | | n^2-7n+10= | | 30-15=45+s | | 2(1-8c)=5-3(6c+1)+4c | | (2*2/7)+(3*2/14)=n | | 2(6-2y)+3y=8 | | 4x+6x-48=64-6x | | 3x-3+2x=7x-15 | | 7w-2w+8=6w+3w-12 | | 3p+1=8p+6 | | 16x^2-96x=108 | | c-5c^2-25= | | 5x+30=5 | | 2-(1-m)=5n+29 | | x-4=6x-4 | | -6x+10+7x=6+x+4 | | 7t-18=-9+8t | | 150r=12 | | 3.142(16)h= | | 3x-8=-3x-4 | | 34.6+4h/5=8.44 | | 6x+84=12(x+4) | | t=132.99+0.28m | | 5n-26=-34+3n | | 2x+(5y-13)=47 | | 150rR=12 | | x-(2-x)-2x=4-x | | -10+3k=k+4 | | (3x-1)(5x^2-9x+2)= | | 4-(2x+5)=-2(4x+5) |

Equations solver categories