x^2=-7x-1

Simple and best practice solution for x^2=-7x-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 x^2=-7x-1 equation:


Simplifying
x2 = -7x + -1

Reorder the terms:
x2 = -1 + -7x

Solving
x2 = -1 + -7x

Solving for variable 'x'.

Reorder the terms:
1 + 7x + x2 = -1 + -7x + 1 + 7x

Reorder the terms:
1 + 7x + x2 = -1 + 1 + -7x + 7x

Combine like terms: -1 + 1 = 0
1 + 7x + x2 = 0 + -7x + 7x
1 + 7x + x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
1 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 7x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 7x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x + x2 = 0 + -1
7x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
7x + x2 = -1

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -1 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -1 + 12.25

Combine like terms: -1 + 12.25 = 11.25
12.25 + 7x + x2 = 11.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

x + 3.5 = 3.354101966 Simplifying x + 3.5 = 3.354101966 Reorder the terms: 3.5 + x = 3.354101966 Solving 3.5 + x = 3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 3.354101966 + -3.5 x = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 x = -0.145898034 Simplifying x = -0.145898034

Subproblem 2

x + 3.5 = -3.354101966 Simplifying x + 3.5 = -3.354101966 Reorder the terms: 3.5 + x = -3.354101966 Solving 3.5 + x = -3.354101966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -3.354101966 + -3.5 x = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 x = -6.854101966 Simplifying x = -6.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.145898034, -6.854101966}

See similar equations:

| 7x+12=5x | | 8(6a+7b)-11(2b+8a)= | | 44+2x+21+x=180 | | 4t^2-4t+1=0 | | 167-5x=22x+20 | | 5x-2=3x+9 | | 120+X=4X+X | | 9-8x=129-36 | | 2x+x+21=180 | | 9z-5z=30z | | 9-8x=129-36x | | 16.2=-4.2t+1.5 | | 1.2X=20+X | | (x^2+8x)+(y^2+10y)=8 | | 4x+14=-52-7x | | 111=x^2+11 | | 100-6x=2x+12 | | -2a-3(b-4a)= | | 6(2x+3)=42 | | x+x(.10)=110 | | 7t^2-7t+1=0 | | (-5)+9+(-7)= | | 5(2z-1)-2(z+3)=4(z+1) | | 3x^2=5 | | 10y^2+2y^3= | | 3(2x-4)=3x-5(x+1) | | 5x-5=-4+4x | | 4a+6(a+8)= | | 7y-4=4y-13 | | 8(4p-5)-7p=20p-10 | | x+21-2x=136 | | 5x+50=8x+14 |

Equations solver categories