400=.1x^2+3x

Simple and best practice solution for 400=.1x^2+3x 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 400=.1x^2+3x equation:


Simplifying
400 = 0.1x2 + 3x

Reorder the terms:
400 = 3x + 0.1x2

Solving
400 = 3x + 0.1x2

Solving for variable 'x'.

Reorder the terms:
400 + -3x + -0.1x2 = 3x + -3x + 0.1x2 + -0.1x2

Combine like terms: 3x + -3x = 0
400 + -3x + -0.1x2 = 0 + 0.1x2 + -0.1x2
400 + -3x + -0.1x2 = 0.1x2 + -0.1x2

Combine like terms: 0.1x2 + -0.1x2 = 0.0
400 + -3x + -0.1x2 = 0.0

Begin completing the square.  Divide all terms by
-0.1 the coefficient of the squared term: 

Divide each side by '-0.1'.
-4000 + 30x + x2 = 0

Move the constant term to the right:

Add '4000' to each side of the equation.
-4000 + 30x + 4000 + x2 = 0 + 4000

Reorder the terms:
-4000 + 4000 + 30x + x2 = 0 + 4000

Combine like terms: -4000 + 4000 = 0
0 + 30x + x2 = 0 + 4000
30x + x2 = 0 + 4000

Combine like terms: 0 + 4000 = 4000
30x + x2 = 4000

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 4000 + 225

Reorder the terms:
225 + 30x + x2 = 4000 + 225

Combine like terms: 4000 + 225 = 4225
225 + 30x + x2 = 4225

Factor a perfect square on the left side:
(x + 15)(x + 15) = 4225

Calculate the square root of the right side: 65

Break this problem into two subproblems by setting 
(x + 15) equal to 65 and -65.

Subproblem 1

x + 15 = 65 Simplifying x + 15 = 65 Reorder the terms: 15 + x = 65 Solving 15 + x = 65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 65 + -15 Combine like terms: 15 + -15 = 0 0 + x = 65 + -15 x = 65 + -15 Combine like terms: 65 + -15 = 50 x = 50 Simplifying x = 50

Subproblem 2

x + 15 = -65 Simplifying x + 15 = -65 Reorder the terms: 15 + x = -65 Solving 15 + x = -65 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -65 + -15 Combine like terms: 15 + -15 = 0 0 + x = -65 + -15 x = -65 + -15 Combine like terms: -65 + -15 = -80 x = -80 Simplifying x = -80

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50, -80}

See similar equations:

| R(X)=75X-5X^2 | | -54y=54 | | 4a-(a-6)=2+3a | | X+2x-3x=30 | | 29=83z | | 12-6n+2n=5n-42 | | 17.5x=0.5223475+30x | | 70-3n=5n+8 | | 5y-2+y=70+3y-5y | | 47=25t | | 3m-9=8-10m | | 10x+3=8x+19 | | 5h-2(1.5+4)=10 | | P+(-9)=-6 | | 7x-3(2x-1)+4=6x-3(x+1) | | z^2-2z-143=0 | | 2x+3(-3z+3)-z=1 | | 5h-2(0.75h+4)=10 | | 7=px^2+qx | | abs(x+3)+abs(4-x)=7 | | 3u^2-26u+16=0 | | y=px^2+qx | | 22=4+3w | | 6(2n-3)=(8n+7)+4 | | P-6=6p+9 | | -x^2-sinx-1=0 | | n^2+2n-90=0 | | 26x-7-17x=3(3x-3)+2 | | 5(x+3)=10x-20 | | 6x+ky=6 | | 3x+47=9x-7 | | 9x^2+42x-180=0 |

Equations solver categories