2x+3x^2=380

Simple and best practice solution for 2x+3x^2=380 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 2x+3x^2=380 equation:


Simplifying
2x + 3x2 = 380

Solving
2x + 3x2 = 380

Solving for variable 'x'.

Reorder the terms:
-380 + 2x + 3x2 = 380 + -380

Combine like terms: 380 + -380 = 0
-380 + 2x + 3x2 = 0

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

Divide each side by '3'.
-126.6666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '126.6666667' to each side of the equation.
-126.6666667 + 0.6666666667x + 126.6666667 + x2 = 0 + 126.6666667

Reorder the terms:
-126.6666667 + 126.6666667 + 0.6666666667x + x2 = 0 + 126.6666667

Combine like terms: -126.6666667 + 126.6666667 = 0.0000000
0.0000000 + 0.6666666667x + x2 = 0 + 126.6666667
0.6666666667x + x2 = 0 + 126.6666667

Combine like terms: 0 + 126.6666667 = 126.6666667
0.6666666667x + x2 = 126.6666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 126.6666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 126.6666667 + 0.1111111112

Combine like terms: 126.6666667 + 0.1111111112 = 126.7777778112
0.1111111112 + 0.6666666667x + x2 = 126.7777778112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 126.7777778112

Calculate the square root of the right side: 11.259563838

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 11.259563838 and -11.259563838.

Subproblem 1

x + 0.3333333334 = 11.259563838 Simplifying x + 0.3333333334 = 11.259563838 Reorder the terms: 0.3333333334 + x = 11.259563838 Solving 0.3333333334 + x = 11.259563838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 11.259563838 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 11.259563838 + -0.3333333334 x = 11.259563838 + -0.3333333334 Combine like terms: 11.259563838 + -0.3333333334 = 10.9262305046 x = 10.9262305046 Simplifying x = 10.9262305046

Subproblem 2

x + 0.3333333334 = -11.259563838 Simplifying x + 0.3333333334 = -11.259563838 Reorder the terms: 0.3333333334 + x = -11.259563838 Solving 0.3333333334 + x = -11.259563838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -11.259563838 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -11.259563838 + -0.3333333334 x = -11.259563838 + -0.3333333334 Combine like terms: -11.259563838 + -0.3333333334 = -11.5928971714 x = -11.5928971714 Simplifying x = -11.5928971714

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.9262305046, -11.5928971714}

See similar equations:

| x*14=105 | | 2Q+3q^2=380 | | -1/2(32)x^2+40x+80=104.64 | | 3x+38=5x+20 | | 3(3F-5)=4F-11 | | 13.5+.5x=x | | 1/2(4x+15)1/2 | | 2(x-3)-2(x+4)=24 | | 1+(-x)forx=-1.7 | | 40+1.5x=80 | | 3.6+(-t)fort=-1.7 | | 40x+1.5x=80x | | 2x+3y=12y | | 5w-6=2+3 | | 2x+3y=12fory | | 200+5x=150+7x | | 298.90+68.7m=74.80m | | x+2x=1.05 | | x+3(3x-5)=2(5x-7) | | A=p+pt | | -7(0.2x+0.4)-1.8=0.4 | | 4x^2-36x+77=0 | | x+12.5=17.25 | | 5+5+5=625 | | -.01x^2+0.6x=-5.2 | | 5+5+5=525 | | -9n^2+7n+4=0 | | 5m-10=20 | | 7(3x+5)=-11(x+9) | | (4x+2)(x+5)=48 | | 3x^2-16x+19= | | 3k^2+17k+20= |

Equations solver categories