x^2+1=-3x

Simple and best practice solution for x^2+1=-3x 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+1=-3x equation:


Simplifying
x2 + 1 = -3x

Reorder the terms:
1 + x2 = -3x

Solving
1 + x2 = -3x

Solving for variable 'x'.

Reorder the terms:
1 + 3x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
1 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x + x2 = 0 + -1
3x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3x + x2 = -1

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -1 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + 3x + x2 = 1.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1.5 = 1.118033989 Simplifying x + 1.5 = 1.118033989 Reorder the terms: 1.5 + x = 1.118033989 Solving 1.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.118033989 + -1.5 x = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 x = -0.381966011 Simplifying x = -0.381966011

Subproblem 2

x + 1.5 = -1.118033989 Simplifying x + 1.5 = -1.118033989 Reorder the terms: 1.5 + x = -1.118033989 Solving 1.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.118033989 + -1.5 x = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 x = -2.618033989 Simplifying x = -2.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.381966011, -2.618033989}

See similar equations:

| y+9=180 | | 5(ln(x))+5=0 | | 0.072=w-4.9 | | (3x)/10=(5x)/6 | | y+9+x+8=180 | | 3.5=4-3(x) | | 4x+5(4x-10)=94 | | 19*8+52= | | y=10-2 | | -15=4-3(x) | | (200)y=6000 | | 4x+3(x+16)=176 | | W^2+8w=84 | | 8y+9=73 | | 4.12w=70.04 | | 1.00=0.5*x | | -3(1+2b)+7=-23+3b | | (2m+3)(4m+3)= | | 64-255x^2-4x^4=0 | | 7x+45=45 | | a+14+6a+4=180 | | 104/x=13/2 | | 7x+2(4x+18)=156 | | 85+6x=193 | | v=-12 | | -7(-3x-1)=27 | | -7=1+2k-4k | | 11=0.75-1 | | 9b+8+10b+1=180 | | 3x-9+x=x+18 | | 10x^2+6x=108 | | X+(-32)=46 |

Equations solver categories