x^2-6x+7=0

Simple and best practice solution for x^2-6x+7=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^2-6x+7=0 equation: 


Simplifying
x2 + -6x + 7 = 0

Reorder the terms:
7 + -6x + x2 = 0

Solving
7 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x + x2 = 0 + -7
-6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6x + x2 = -7

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 = -7 + 9

Reorder the terms:
9 + -6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + -6x + x2 = 2

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -3) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -3 = 1.414213562

Simplifying
x + -3 = 1.414213562

Reorder the terms:
-3 + x = 1.414213562

Solving
-3 + x = 1.414213562

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 = 1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.414213562 + 3
x = 1.414213562 + 3

Combine like terms: 1.414213562 + 3 = 4.414213562
x = 4.414213562

Simplifying
x = 4.414213562


Subproblem 2
x + -3 = -1.414213562

Simplifying
x + -3 = -1.414213562

Reorder the terms:
-3 + x = -1.414213562

Solving
-3 + x = -1.414213562

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 = -1.414213562 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.414213562 + 3
x = -1.414213562 + 3

Combine like terms: -1.414213562 + 3 = 1.585786438
x = 1.585786438

Simplifying
x = 1.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.414213562, 1.585786438}

See similar equations:

| 3x-4=(x+1) | | 5(x-3)=2x+6 | | 4y-1=2y-7 | | 8x^2-32x^3+7=0 | | 7x^2-12x=0 | | x^2+9y^2-18y=0 | | k=8 | | 6600+13v=7800 | | 2x-1=x-7 | | 5(y+3)=20 | | 7-2y=-21 | | 9-3y=6 | | 3a-5=-26 | | -7x-9y-2x+6y= | | -2+3+y=3 | | 15-6=3t | | 2a-6=4 | | t-4=-2 | | -2+k=0 | | 5r=40 | | 19-a=30 | | 4-b=6-4 | | u+1+2=5 | | 6y=20-2 | | d-5=-3 | | 0.5n=1 | | 15-a=20 | | 14=x+4 | | 5+v=4+3 | | 2(h+1)=6 | | 7-t+1=6 | | 1x+10y=50 |

Equations solver categories