x^2-10x=78

Simple and best practice solution for x^2-10x=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 x^2-10x=78 equation:


Simplifying
x2 + -10x = 78

Reorder the terms:
-10x + x2 = 78

Solving
-10x + x2 = 78

Solving for variable 'x'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '78' to each side of the equation.
-78 + -10x + 78 + x2 = 0 + 78

Reorder the terms:
-78 + 78 + -10x + x2 = 0 + 78

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

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

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 78 + 25

Reorder the terms:
25 + -10x + x2 = 78 + 25

Combine like terms: 78 + 25 = 103
25 + -10x + x2 = 103

Factor a perfect square on the left side:
(x + -5)(x + -5) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(x + -5) equal to 10.148891565 and -10.148891565.

Subproblem 1

x + -5 = 10.148891565 Simplifying x + -5 = 10.148891565 Reorder the terms: -5 + x = 10.148891565 Solving -5 + x = 10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.148891565 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.148891565 + 5 x = 10.148891565 + 5 Combine like terms: 10.148891565 + 5 = 15.148891565 x = 15.148891565 Simplifying x = 15.148891565

Subproblem 2

x + -5 = -10.148891565 Simplifying x + -5 = -10.148891565 Reorder the terms: -5 + x = -10.148891565 Solving -5 + x = -10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.148891565 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.148891565 + 5 x = -10.148891565 + 5 Combine like terms: -10.148891565 + 5 = -5.148891565 x = -5.148891565 Simplifying x = -5.148891565

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.148891565, -5.148891565}

See similar equations:

| x+(x+3)=121 | | 0=10x+2x^2 | | 4x^2=21 | | 30v=60 | | 53-5x=22x+17 | | 4m+2n=6 | | 7x+4(-x+13)=16 | | x+(x+2)=122 | | 5n^2-45n+11=0 | | 1+(1+2)=122 | | 18y-13y=-100-5y | | 18600x+68600x= | | 7x+4=54+3x | | (2x+7)(2x-7)=1 | | 186000x=68600x | | 5x-3=-3x+45 | | 18+2x=-10-2x | | 11x-4=4x+52 | | a^4-4a^3*b+b^2= | | 3-(x-4)=7-x | | 6-(-5b)=5b-3 | | 60-10m=-18m-4 | | 3(x+2)-2(2x-4)=38 | | 25+7=10s-7 | | 6x+12=4x+45 | | y-(y*.10)=12000 | | 12x-6=8+6x | | -r+2=20+5r | | 6v+8=-4-v | | 40a+56b= | | w^2-12w+17=0 | | 3(2g-5)=4g+13 |

Equations solver categories