.5(x+20)(x)=78

Simple and best practice solution for .5(x+20)(x)=78 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 .5(x+20)(x)=78 equation: 


Simplifying
0.5(x + 20)(x) = 78

Reorder the terms:
0.5(20 + x)(x) = 78

Reorder the terms for easier multiplication:
0.5x(20 + x) = 78
(20 * 0.5x + x * 0.5x) = 78
(10x + 0.5x2) = 78

Solving
10x + 0.5x2 = 78

Solving for variable 'x'.

Reorder the terms:
-78 + 10x + 0.5x2 = 78 + -78

Combine like terms: 78 + -78 = 0
-78 + 10x + 0.5x2 = 0

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
-156 + 20x + x2 = 0

Move the constant term to the right:

Add '156' to each side of the equation.
-156 + 20x + 156 + x2 = 0 + 156

Reorder the terms:
-156 + 156 + 20x + x2 = 0 + 156

Combine like terms: -156 + 156 = 0
0 + 20x + x2 = 0 + 156
20x + x2 = 0 + 156

Combine like terms: 0 + 156 = 156
20x + x2 = 156

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = 156 + 100

Reorder the terms:
100 + 20x + x2 = 156 + 100

Combine like terms: 156 + 100 = 256
100 + 20x + x2 = 256

Factor a perfect square on the left side:
(x + 10)(x + 10) = 256

Calculate the square root of the right side: 16

Break this problem into two subproblems by setting 
(x + 10) equal to 16 and -16.


Subproblem 1
x + 10 = 16

Simplifying
x + 10 = 16

Reorder the terms:
10 + x = 16

Solving
10 + x = 16

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = 16 + -10

Combine like terms: 10 + -10 = 0
0 + x = 16 + -10
x = 16 + -10

Combine like terms: 16 + -10 = 6
x = 6

Simplifying
x = 6


Subproblem 2
x + 10 = -16

Simplifying
x + 10 = -16

Reorder the terms:
10 + x = -16

Solving
10 + x = -16

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x = -16 + -10

Combine like terms: 10 + -10 = 0
0 + x = -16 + -10
x = -16 + -10

Combine like terms: -16 + -10 = -26
x = -26

Simplifying
x = -26


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6, -26}

See similar equations:

| 7(8-9n)= | | -n+12=n^2 | | 40x=15x-100 | | 20000y+2500= | | 7-3x=5x+13x | | .5(x-20)(x)=78 | | -(7x^2-6x+6)= | | 20000+2500=x | | 2x+7=3x+52 | | -8+b-8=-22 | | 2lx+1l-3lx-2l+lx-5l=x+2 | | 8(5j+4)= | | 3(4-x)=18x | | 40x=15-100 | | (8x+2)-(3x-2)= | | 2(x^2)-5x=18 | | Y=50x^2-98 | | 5k(3k+2)= | | 6(4-2x)= | | 112+6x=10x | | lx-4l-5lx-4l+6=0 | | 2(9h+3)= | | 4c(4c+2)= | | 6/5*4/7 | | 1+2m=7 | | 0=-2n+7n | | -(5x^2-2x+2)= | | 4m+zr=r-5h | | 48y-24=6y+6 | | 3x*24+42-3=50 | | p^2=1.142 | | 4x-9[9(x+3)-(x-2)]-6= |

Equations solver categories