2x+3x^2=46

Simple and best practice solution for 2x+3x^2=46 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=46 equation:


Simplifying
2x + 3x2 = 46

Solving
2x + 3x2 = 46

Solving for variable 'x'.

Reorder the terms:
-46 + 2x + 3x2 = 46 + -46

Combine like terms: 46 + -46 = 0
-46 + 2x + 3x2 = 0

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

Divide each side by '3'.
-15.33333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '15.33333333' to each side of the equation.
-15.33333333 + 0.6666666667x + 15.33333333 + x2 = 0 + 15.33333333

Reorder the terms:
-15.33333333 + 15.33333333 + 0.6666666667x + x2 = 0 + 15.33333333

Combine like terms: -15.33333333 + 15.33333333 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 15.33333333
0.6666666667x + x2 = 0 + 15.33333333

Combine like terms: 0 + 15.33333333 = 15.33333333
0.6666666667x + x2 = 15.33333333

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 = 15.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 15.33333333 + 0.1111111112

Combine like terms: 15.33333333 + 0.1111111112 = 15.4444444412
0.1111111112 + 0.6666666667x + x2 = 15.4444444412

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 15.4444444412

Calculate the square root of the right side: 3.92994204

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 3.92994204 and -3.92994204.

Subproblem 1

x + 0.3333333334 = 3.92994204 Simplifying x + 0.3333333334 = 3.92994204 Reorder the terms: 0.3333333334 + x = 3.92994204 Solving 0.3333333334 + x = 3.92994204 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 = 3.92994204 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 3.92994204 + -0.3333333334 x = 3.92994204 + -0.3333333334 Combine like terms: 3.92994204 + -0.3333333334 = 3.5966087066 x = 3.5966087066 Simplifying x = 3.5966087066

Subproblem 2

x + 0.3333333334 = -3.92994204 Simplifying x + 0.3333333334 = -3.92994204 Reorder the terms: 0.3333333334 + x = -3.92994204 Solving 0.3333333334 + x = -3.92994204 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 = -3.92994204 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -3.92994204 + -0.3333333334 x = -3.92994204 + -0.3333333334 Combine like terms: -3.92994204 + -0.3333333334 = -4.2632753734 x = -4.2632753734 Simplifying x = -4.2632753734

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5966087066, -4.2632753734}

See similar equations:

| 2/3/1/6 | | f(x)=x^2-4x-32 | | 4c-3c+7=2c+10 | | 3/8/1/2 | | y=-8+2x+x^2 | | 2m+[8-4m]=28 | | 2(x+1)-3(x-2)=5(x+3) | | 3x^2+27x=-54 | | 9x+15=11x-25 | | 8(x+2)=20(2x-4) | | -10x^2+130x-400=0 | | 0.20x-0.08(x-10)=24 | | 84/4 | | 1/9/2/3 | | 2.9h-5.1/2=7.7 | | -4x-5=6 | | -2x-6=3x+12+7 | | 12x-12=108+12 | | 4x+4y=110 | | 2/7/1/7 | | 35/100 | | -2x-12+6x=4x-12 | | 10=-8+m/4 | | 5m-3+14x=156 | | 8+15m-3=9m+29-2m | | 13v-8v-12=5v-42 | | 4b-10=-2(b+12)-b | | -1*(4+x)=6 | | 36/165 | | (3n-7)/6=(2n+5)/3 | | (1/2)x+6-2x+(1/2)=(7/2) | | 4x+3=4x-3 |

Equations solver categories