x^2+3=-9x

Simple and best practice solution for x^2+3=-9x 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^2+3=-9x equation:


Simplifying
x2 + 3 = -9x

Reorder the terms:
3 + x2 = -9x

Solving
3 + x2 = -9x

Solving for variable 'x'.

Reorder the terms:
3 + 9x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
3 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 9x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 9x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 9x + x2 = 0 + -3
9x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
9x + x2 = -3

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -3 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -3 + 20.25

Combine like terms: -3 + 20.25 = 17.25
20.25 + 9x + x2 = 17.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.153311931 and -4.153311931.

Subproblem 1

x + 4.5 = 4.153311931 Simplifying x + 4.5 = 4.153311931 Reorder the terms: 4.5 + x = 4.153311931 Solving 4.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.153311931 + -4.5 x = 4.153311931 + -4.5 Combine like terms: 4.153311931 + -4.5 = -0.346688069 x = -0.346688069 Simplifying x = -0.346688069

Subproblem 2

x + 4.5 = -4.153311931 Simplifying x + 4.5 = -4.153311931 Reorder the terms: 4.5 + x = -4.153311931 Solving 4.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -4.153311931 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.153311931 + -4.5 x = -4.153311931 + -4.5 Combine like terms: -4.153311931 + -4.5 = -8.653311931 x = -8.653311931 Simplifying x = -8.653311931

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.346688069, -8.653311931}

See similar equations:

| 4+2x-3x=-3 | | -20x+14=-8x+44 | | X-5*2=x+15 | | 8e+2e-6=34 | | 17y-6=15 | | 3y=-3x+5 | | 230=3.5a+50 | | [10-3m]=11 | | 12=360-4q | | 3y+1=8x-61 | | X+y=1130 | | Md=2p | | X-5=x+15 | | 50x+10y+z=100 | | 4(2x+5)8=36 | | -144.4=-0.6p | | 2x-4(0)=4 | | 7.15=0.3p+4.5 | | [-6-2x]=4 | | 10+5x=80 | | 23+3n=-(5n-7) | | 6x+3=7x+8 | | 3x+9+4x=79 | | 7.15=0.3(p+4.5) | | 5x+2x+9x-4x+3x-x= | | -144.4=0.6p | | 19.5+.5t=10.6206+-.4t | | 48(x^3)-32(x^2)-3x+2=0 | | 7a+33+5a-9=180 | | y-3x=-12 | | Pmb=360-4q | | 70=2x+y+2x+2y |

Equations solver categories