x^2+6x=14

Simple and best practice solution for x^2+6x=14 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+6x=14 equation:


Simplifying
x2 + 6x = 14

Reorder the terms:
6x + x2 = 14

Solving
6x + x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + 6x + x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 6x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 6x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 6x + x2 = 0 + 14
6x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
6x + x2 = 14

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 14 + 9

Reorder the terms:
9 + 6x + x2 = 14 + 9

Combine like terms: 14 + 9 = 23
9 + 6x + x2 = 23

Factor a perfect square on the left side:
(x + 3)(x + 3) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + 3) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + 3 = 4.795831523 Simplifying x + 3 = 4.795831523 Reorder the terms: 3 + x = 4.795831523 Solving 3 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.795831523 + -3 x = 4.795831523 + -3 Combine like terms: 4.795831523 + -3 = 1.795831523 x = 1.795831523 Simplifying x = 1.795831523

Subproblem 2

x + 3 = -4.795831523 Simplifying x + 3 = -4.795831523 Reorder the terms: 3 + x = -4.795831523 Solving 3 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.795831523 + -3 x = -4.795831523 + -3 Combine like terms: -4.795831523 + -3 = -7.795831523 x = -7.795831523 Simplifying x = -7.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.795831523, -7.795831523}

See similar equations:

| 9-6a=1-4a | | -57-3x=13-10x | | 3x+5=5x-16 | | 3x+6x-45=0 | | 8x-8=2x-2 | | 100x-9x=451 | | 4-10x=5x+8 | | 3x+37=11x-51 | | 11+2(9)=11+8 | | 0.90x+.05(6-x)=.10(71) | | 6x-1= | | 3*x+61=7*x+13 | | 3(2X+10)=60 | | 12x^2-8x=-1 | | 8*x+8=3*x+38 | | 2x+19= | | 26+5y=8y-16 | | x^2-2x-120=0 | | 11*x-17=82 | | 4x-1=6x-15 | | 3X+45=90 | | 19+1897= | | 0.625x^2-0.125x-1=0 | | (3x^2-4x+20)-(4x^2-3x-20)= | | -2w+2=-8+19 | | 0.625x^2-0.125-1=0 | | 4-x=5x+8 | | 3x+19=13x-71 | | 3x(x-5)=0 | | -124-10x=10x+16 | | -x^4+4=40-21-x | | 3X+45-x=90 |

Equations solver categories