x(2x-10)=400

Simple and best practice solution for x(2x-10)=400 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(2x-10)=400 equation: 


Simplifying
x(2x + -10) = 400

Reorder the terms:
x(-10 + 2x) = 400
(-10 * x + 2x * x) = 400
(-10x + 2x2) = 400

Solving
-10x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -10x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + -5x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-200 + -5x + x2)' equal to zero and attempt to solve:

Simplifying
-200 + -5x + x2 = 0

Solving
-200 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -5x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + -5x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -5x + x2 = 0 + 200
-5x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
-5x + x2 = 200

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 200 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 200 + 6.25

Combine like terms: 200 + 6.25 = 206.25
6.25 + -5x + x2 = 206.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(x + -2.5) equal to 14.361406616 and -14.361406616.


Subproblem 1
x + -2.5 = 14.361406616

Simplifying
x + -2.5 = 14.361406616

Reorder the terms:
-2.5 + x = 14.361406616

Solving
-2.5 + x = 14.361406616

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 14.361406616 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 14.361406616 + 2.5
x = 14.361406616 + 2.5

Combine like terms: 14.361406616 + 2.5 = 16.861406616
x = 16.861406616

Simplifying
x = 16.861406616


Subproblem 2
x + -2.5 = -14.361406616

Simplifying
x + -2.5 = -14.361406616

Reorder the terms:
-2.5 + x = -14.361406616

Solving
-2.5 + x = -14.361406616

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -14.361406616 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -14.361406616 + 2.5
x = -14.361406616 + 2.5

Combine like terms: -14.361406616 + 2.5 = -11.861406616
x = -11.861406616

Simplifying
x = -11.861406616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.861406616, -11.861406616}
Solution
x = {16.861406616, -11.861406616}

See similar equations:

| 10x=-16+36 | | (5x-3)(x+1)=2x | | -6(x-3)=9 | | 3t-6t-8-7t=-2 | | 0.50x+0.25(50)=42.5 | | 3[5x-(3-x)]=3(3x-4) | | 4x^2+9y^2=36 | | 0.50+0.25(50)=42.5 | | 3y+6x-12=0 | | 4a/5+7=11 | | 2x+5=-26 | | 5u-10=3u | | 4x(x-1)=(x-2)(2x+3) | | 109-(6x+16)=6(x+9)+x | | -4=-4(x+3) | | 100(2+m)=500 | | 2(3x-2)-2x=5x+6 | | 3(3x-8)=35 | | 8t-9=y | | -2(5x+1)=8 | | 9x-23+2x=43 | | 8-5x=4-3x | | (17/13)=(v/7) | | 10x-19=24 | | -2k+k=-k+2 | | 1+2x-2-5=4-3x | | 2x+3y=40.5 | | 8u-37=5(u-5) | | 8-x=8+7x-5x | | 15x-25=4x+63 | | 3(-5k+5)=120 | | 4t-5=z |

Equations solver categories