x^2+14(x)+47=0

Simple and best practice solution for x^2+14(x)+47=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+14(x)+47=0 equation: 


Simplifying
x2 + 14(x) + 47 = 0

Reorder the terms:
47 + 14x + x2 = 0

Solving
47 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + 14x + -47 + x2 = 0 + -47

Reorder the terms:
47 + -47 + 14x + x2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 14x + x2 = 0 + -47
14x + x2 = 0 + -47

Combine like terms: 0 + -47 = -47
14x + x2 = -47

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -47 + 49

Reorder the terms:
49 + 14x + x2 = -47 + 49

Combine like terms: -47 + 49 = 2
49 + 14x + x2 = 2

Factor a perfect square on the left side:
(x + 7)(x + 7) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 7) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 7 = 1.414213562

Simplifying
x + 7 = 1.414213562

Reorder the terms:
7 + x = 1.414213562

Solving
7 + x = 1.414213562

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = 1.414213562 + -7

Combine like terms: 7 + -7 = 0
0 + x = 1.414213562 + -7
x = 1.414213562 + -7

Combine like terms: 1.414213562 + -7 = -5.585786438
x = -5.585786438

Simplifying
x = -5.585786438


Subproblem 2
x + 7 = -1.414213562

Simplifying
x + 7 = -1.414213562

Reorder the terms:
7 + x = -1.414213562

Solving
7 + x = -1.414213562

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + x = -1.414213562 + -7

Combine like terms: 7 + -7 = 0
0 + x = -1.414213562 + -7
x = -1.414213562 + -7

Combine like terms: -1.414213562 + -7 = -8.414213562
x = -8.414213562

Simplifying
x = -8.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.585786438, -8.414213562}

See similar equations:

| 2(4x-8)-4(x-8)= | | 4x-7=2x+3 | | 5s-2s^2=0 | | 3x(2x-9)=15 | | (q+4)(3q-15)=0 | | (w+8)(-11)= | | x(x-24)=0 | | 6y+6=8y | | -2x+58=-8 | | 7y-6(5y-6)=0 | | 36w^2-16=0 | | 4y+12=5y | | 32+y=40 | | 5x^2-36x+7=0 | | x-14=-38 | | 9x^2-3x-20=0 | | 6+2w=42 | | z^2-z-20=0 | | x^2+11x-28=0 | | 20=c(c-8) | | 7y+-2x=5 | | 14s^2-33s+18=0 | | 4a^2+15-16a=0 | | 72=-8(4x-5) | | 4b^2-2=322 | | 5m=13 | | 8x^2-3x+2=7x^2 | | 7x+-2y=5 | | 500=9w+2l | | 5-3x=5x-11 | | z^4-37z^2+36=0 | | x-8=4-x |

Equations solver categories