6x=-9x^2+1

Simple and best practice solution for 6x=-9x^2+1 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 6x=-9x^2+1 equation:


Simplifying
6x = -9x2 + 1

Reorder the terms:
6x = 1 + -9x2

Solving
6x = 1 + -9x2

Solving for variable 'x'.

Reorder the terms:
-1 + 6x + 9x2 = 1 + -9x2 + -1 + 9x2

Reorder the terms:
-1 + 6x + 9x2 = 1 + -1 + -9x2 + 9x2

Combine like terms: 1 + -1 = 0
-1 + 6x + 9x2 = 0 + -9x2 + 9x2
-1 + 6x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-1 + 6x + 9x2 = 0

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

Divide each side by '9'.
-0.1111111111 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + 0.6666666667x + 0.1111111111 + x2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + 0.6666666667x + x2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + 0.6666666667x + x2 = 0 + 0.1111111111
0.6666666667x + x2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
0.6666666667x + x2 = 0.1111111111

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 = 0.1111111111 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 0.1111111111 + 0.1111111112

Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223
0.1111111112 + 0.6666666667x + x2 = 0.2222222223

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 0.2222222223

Calculate the square root of the right side: 0.471404521

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 0.471404521 and -0.471404521.

Subproblem 1

x + 0.3333333334 = 0.471404521 Simplifying x + 0.3333333334 = 0.471404521 Reorder the terms: 0.3333333334 + x = 0.471404521 Solving 0.3333333334 + x = 0.471404521 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 = 0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.471404521 + -0.3333333334 x = 0.471404521 + -0.3333333334 Combine like terms: 0.471404521 + -0.3333333334 = 0.1380711876 x = 0.1380711876 Simplifying x = 0.1380711876

Subproblem 2

x + 0.3333333334 = -0.471404521 Simplifying x + 0.3333333334 = -0.471404521 Reorder the terms: 0.3333333334 + x = -0.471404521 Solving 0.3333333334 + x = -0.471404521 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 = -0.471404521 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.471404521 + -0.3333333334 x = -0.471404521 + -0.3333333334 Combine like terms: -0.471404521 + -0.3333333334 = -0.8047378544 x = -0.8047378544 Simplifying x = -0.8047378544

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1380711876, -0.8047378544}

See similar equations:

| 42x^2+42+91x=0 | | y=2x^2-13x | | 7+k+5=10 | | 1/2-2/2 | | 22x+3=10x-8 | | 99+36x^2-216x=0 | | -9x^2=-12+5x-7x^2 | | (n-8)-(-2+2)= | | 1X^2+6X+1Y^2+4Y+4=0 | | Sqrtx-3=17 | | 1/2x-4/5= | | 8(t+7)= | | 4x^2-5+4x=0 | | (5x+2)=37 | | 7=4x^2+43 | | -4v=-8v+4v | | m+20=100 | | 7z+2z+4z-7z+4z=10 | | .33-7=.83 | | 2a^2/b^2 | | -4v=-8v | | 15y+2=8whatisy | | 15(13.13-1.33y)+20y=197 | | -6(2k+1)+4=-2+4k | | 10(x+2)=10(x+9) | | 10k+2k-6k-4k=12 | | 0=-10s+10s | | z+60=5z | | t+4=t-10 | | 10-7r=5(3r+2) | | 6=m-(-2) | | t+4=t-1-0 |

Equations solver categories