X^2+10X+1=0

Simple and best practice solution for X^2+10X+1=0 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+10X+1=0 equation:


Simplifying
X2 + 10X + 1 = 0

Reorder the terms:
1 + 10X + X2 = 0

Solving
1 + 10X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 10X + -1 + X2 = 0 + -1

Reorder the terms:
1 + -1 + 10X + X2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10X + X2 = 0 + -1
10X + X2 = 0 + -1

Combine like terms: 0 + -1 = -1
10X + X2 = -1

The X term is 10X.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10X + 25 + X2 = -1 + 25

Reorder the terms:
25 + 10X + X2 = -1 + 25

Combine like terms: -1 + 25 = 24
25 + 10X + X2 = 24

Factor a perfect square on the left side:
(X + 5)(X + 5) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(X + 5) equal to 4.898979486 and -4.898979486.

Subproblem 1

X + 5 = 4.898979486 Simplifying X + 5 = 4.898979486 Reorder the terms: 5 + X = 4.898979486 Solving 5 + X = 4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + X = 4.898979486 + -5 X = 4.898979486 + -5 Combine like terms: 4.898979486 + -5 = -0.101020514 X = -0.101020514 Simplifying X = -0.101020514

Subproblem 2

X + 5 = -4.898979486 Simplifying X + 5 = -4.898979486 Reorder the terms: 5 + X = -4.898979486 Solving 5 + X = -4.898979486 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = -4.898979486 + -5 Combine like terms: 5 + -5 = 0 0 + X = -4.898979486 + -5 X = -4.898979486 + -5 Combine like terms: -4.898979486 + -5 = -9.898979486 X = -9.898979486 Simplifying X = -9.898979486

Solution

The solution to the problem is based on the solutions from the subproblems. X = {-0.101020514, -9.898979486}

See similar equations:

| 5i+9=i-23 | | -9.6-2x=10.8 | | 68=5n+43 | | 2x-4=9x+25 | | 12x+5=6x | | 4x+29=14x-61 | | 12x-1=10x+5 | | 20s^2+s=12 | | 6n+2=4n+17 | | y+5=2y-10 | | (4t-7)=2(t+1)+2 | | 8x-7=89 | | 117-6x=21x+21 | | 8-9x=83-44x | | -51-7x=10x+17 | | -x+46=27 | | 5+2(x-8)=8-8(x-3) | | 99-4x=3x+15 | | 9z-45=45 | | 4x^3-8x^2-9x+18=0 | | 4x+12=93-5x | | 4(x-2)-28=0 | | 5(x+7)-3(2x+1)=35 | | 5-4a=a-13 | | 98-7x=20x+23 | | 3x+7=2r | | 4r+16=-80 | | 3m+2m-2n-5m+5n= | | 2n+8=32 | | 5m-5m= | | 24h=9h+150 | | 10-9x=55-30x |

Equations solver categories