x^2-10x-400=0

Simple and best practice solution for x^2-10x-400=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^2-10x-400=0 equation:


Simplifying
x2 + -10x + -400 = 0

Reorder the terms:
-400 + -10x + x2 = 0

Solving
-400 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '400' to each side of the equation.
-400 + -10x + 400 + x2 = 0 + 400

Reorder the terms:
-400 + 400 + -10x + x2 = 0 + 400

Combine like terms: -400 + 400 = 0
0 + -10x + x2 = 0 + 400
-10x + x2 = 0 + 400

Combine like terms: 0 + 400 = 400
-10x + x2 = 400

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 = 400 + 25

Reorder the terms:
25 + -10x + x2 = 400 + 25

Combine like terms: 400 + 25 = 425
25 + -10x + x2 = 425

Factor a perfect square on the left side:
(x + -5)(x + -5) = 425

Calculate the square root of the right side: 20.615528128

Break this problem into two subproblems by setting 
(x + -5) equal to 20.615528128 and -20.615528128.

Subproblem 1

x + -5 = 20.615528128 Simplifying x + -5 = 20.615528128 Reorder the terms: -5 + x = 20.615528128 Solving -5 + x = 20.615528128 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 = 20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + x = 20.615528128 + 5 x = 20.615528128 + 5 Combine like terms: 20.615528128 + 5 = 25.615528128 x = 25.615528128 Simplifying x = 25.615528128

Subproblem 2

x + -5 = -20.615528128 Simplifying x + -5 = -20.615528128 Reorder the terms: -5 + x = -20.615528128 Solving -5 + x = -20.615528128 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 = -20.615528128 + 5 Combine like terms: -5 + 5 = 0 0 + x = -20.615528128 + 5 x = -20.615528128 + 5 Combine like terms: -20.615528128 + 5 = -15.615528128 x = -15.615528128 Simplifying x = -15.615528128

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.615528128, -15.615528128}

See similar equations:

| 5x+3+4x=3(3x-2) | | 6y=4x+36.25 | | x/455=120/100 | | 16+17k^2+4k= | | 39+19b=100 | | 2n=5/25 | | x-(0.1x)=300 | | (3r+5)/2=13 | | 2y+3x=130 | | n^2+25n+66=0 | | 9x-31=12x+11 | | 5/13r=45/32 | | 12-4/5(-5+15)=4 | | 9(x-3)+7=52 | | 1.8c+32=40 | | -10-20x+35x-14=3x+9x | | 10-6x=30-104 | | b^2+6b+72=72 | | -1/2v=-9/10 | | 2/3r=0 | | 25x^2+4(0)=9 | | 3t-4fort=8 | | 1/2m=6t | | ax^2-4a^2x+4a^3=0 | | 6x+4x=50 | | 10*6=-5*3m | | -26-9x=-6x+52 | | v+3=7+3v+3-v | | -3+14+4x=4+x+10 | | 2X-16=35 | | -6(x-3)+4x=-36 | | 4x+3y=-39 |

Equations solver categories