7x^2-28x+7=0

Simple and best practice solution for 7x^2-28x+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 7x^2-28x+7=0 equation: 


Simplifying
7x2 + -28x + 7 = 0

Reorder the terms:
7 + -28x + 7x2 = 0

Solving
7 + -28x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(1 + -4x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(1 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
1 + -4x + x2 = 0

Solving
1 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x + x2 = 0 + -1
-4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4x + x2 = -1

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + -4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4x + x2 = 3

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

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -2) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -2 = 1.732050808

Simplifying
x + -2 = 1.732050808

Reorder the terms:
-2 + x = 1.732050808

Solving
-2 + x = 1.732050808

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.732050808 + 2
x = 1.732050808 + 2

Combine like terms: 1.732050808 + 2 = 3.732050808
x = 3.732050808

Simplifying
x = 3.732050808


Subproblem 2
x + -2 = -1.732050808

Simplifying
x + -2 = -1.732050808

Reorder the terms:
-2 + x = -1.732050808

Solving
-2 + x = -1.732050808

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.732050808 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.732050808 + 2
x = -1.732050808 + 2

Combine like terms: -1.732050808 + 2 = 0.267949192
x = 0.267949192

Simplifying
x = 0.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.732050808, 0.267949192}
Solution
x = {3.732050808, 0.267949192}

See similar equations:

| -x^2+7=0 | | 3(-4lnx)=6 | | 3x^3y+12x^2y^2-36xy^3=0 | | 3-4lnx=6 | | y=-(0)-4 | | y=3(-2)+1 | | y=3(0)+1 | | 8x^2+16x-24=0 | | (8k+13)-(6K+5)= | | y=3(1)+1 | | 5.7=12.2 | | y-5=12.2 | | -23p-24=-p^2 | | y-5.7=12.2 | | .5n+6=1n+2 | | 32=-4x+8 | | 47x+4=58 | | -3m^2-108= | | n^2=64 | | ln(x-9)-ln(x+7)=ln(x-6)-ln(x+7) | | 12-6r=2r | | 0.67+0.14t=1.70t-0.37 | | -2x-15=-x^2 | | y-5*7=12.2 | | 5x-3+x=3 | | -4a/5-3=7 | | 5r^2=35 | | -7.3x=-146 | | 10t-t+6t= | | -7*3x=-146.0 | | 7x+3=6x | | -7.3x=-146.0 |

Equations solver categories