x+5x^2+6=15-31x

Simple and best practice solution for x+5x^2+6=15-31x 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+5x^2+6=15-31x equation:


Simplifying
x + 5x2 + 6 = 15 + -31x

Reorder the terms:
6 + x + 5x2 = 15 + -31x

Solving
6 + x + 5x2 = 15 + -31x

Solving for variable 'x'.

Reorder the terms:
6 + -15 + x + 31x + 5x2 = 15 + -31x + -15 + 31x

Combine like terms: 6 + -15 = -9
-9 + x + 31x + 5x2 = 15 + -31x + -15 + 31x

Combine like terms: x + 31x = 32x
-9 + 32x + 5x2 = 15 + -31x + -15 + 31x

Reorder the terms:
-9 + 32x + 5x2 = 15 + -15 + -31x + 31x

Combine like terms: 15 + -15 = 0
-9 + 32x + 5x2 = 0 + -31x + 31x
-9 + 32x + 5x2 = -31x + 31x

Combine like terms: -31x + 31x = 0
-9 + 32x + 5x2 = 0

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

Divide each side by '5'.
-1.8 + 6.4x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 6.4x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 6.4x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 6.4x + x2 = 0 + 1.8
6.4x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
6.4x + x2 = 1.8

The x term is 6.4x.  Take half its coefficient (3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
6.4x + 10.24 + x2 = 1.8 + 10.24

Reorder the terms:
10.24 + 6.4x + x2 = 1.8 + 10.24

Combine like terms: 1.8 + 10.24 = 12.04
10.24 + 6.4x + x2 = 12.04

Factor a perfect square on the left side:
(x + 3.2)(x + 3.2) = 12.04

Calculate the square root of the right side: 3.469870315

Break this problem into two subproblems by setting 
(x + 3.2) equal to 3.469870315 and -3.469870315.

Subproblem 1

x + 3.2 = 3.469870315 Simplifying x + 3.2 = 3.469870315 Reorder the terms: 3.2 + x = 3.469870315 Solving 3.2 + x = 3.469870315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 3.469870315 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 3.469870315 + -3.2 x = 3.469870315 + -3.2 Combine like terms: 3.469870315 + -3.2 = 0.269870315 x = 0.269870315 Simplifying x = 0.269870315

Subproblem 2

x + 3.2 = -3.469870315 Simplifying x + 3.2 = -3.469870315 Reorder the terms: 3.2 + x = -3.469870315 Solving 3.2 + x = -3.469870315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -3.469870315 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -3.469870315 + -3.2 x = -3.469870315 + -3.2 Combine like terms: -3.469870315 + -3.2 = -6.669870315 x = -6.669870315 Simplifying x = -6.669870315

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.269870315, -6.669870315}

See similar equations:

| solvex+5x^2+6=15-31x | | -6y+2y=-2 | | 2*x^3+6*x^2+9*x-16=0 | | 2*x^3+3*x-21=0 | | C=2(3.14)14 | | 6x+30y=24 | | ex+5=2 | | 1.5x-2.5y=8.5 | | 9x-20y=6 | | 8x+9y=42 | | f+8=3 | | 100=3y+(2y+5) | | 9+9+4= | | 6y(5-3/8y) | | a^3+3a^2+a+3=0 | | v/5=12.5 | | x/-5=95/15 | | 1.3+0.9x=2+.4x | | 5z^3+3z^2+5z+3=0 | | (b^3+8c^3)(b-2c)(b^2+2bc+4c^2)= | | 4x+2x=13-3 | | ((64y^6)/(x^-3))^(1/3) | | (2b-1)(2b-1)(2b-1)(2b-1)(2b-1)(2b-1)(2b-1)= | | 2x+5=16x^2-48x+36 | | (2x+y-32)(2x+y+32)= | | y^4(y^2+2y-4)= | | d/dx(e^x(cosx)) | | (ab^2-c^3)(ab^2+c^3)= | | 3(2x+5)=4(25+2y) | | (3-x^2)(9+3x^2+x^4)(27+x^6)= | | (7)(9+3x^2+x^4)(27+x^6)= | | 3x+31=7x-1 |

Equations solver categories