7x^2-42x+49=0

Simple and best practice solution for 7x^2-42x+49=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^2-42x+49=0 equation: 


Simplifying
7x2 + -42x + 49 = 0

Reorder the terms:
49 + -42x + 7x2 = 0

Solving
49 + -42x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(7 + -6x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(7 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x + x2 = 0

Solving
7 + -6x + x2 = 0

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}
Solution
x = {4.414213562, 1.585786438}

See similar equations:

| 2(9+-15r+4r^2)=0 | | x^2-x=0-2/3 | | 45-79d-91-9d+8+4d= | | 1/2x2/3/5 | | 9x-4x-19x= | | 13x=-47 | | 4(8x-2)/3=10 | | F(4)=f(4-1)+2(4) | | 2/5=X/12.5 | | 5y=10y+(-5) | | 8x+3=8(x+3) | | 65+6x=11 | | 96=(4*Y)+(6*X) | | 96=(4*Y)+(12*X) | | y=30+10*x | | 5log[2]x+2=12 | | 5(6+3f)+2(2-3f)= | | 4(3q+2)+3(2q+1)= | | (2x-y)(m+5)=m(x-1) | | 4(3q+2)+3(4k+7)= | | 4(2k+3)+3(4k+7)= | | S=2(14*3)+2(14*9)+2(3*9) | | 8y^2+18y=36 | | log(x^2-1)= | | 12-8y+6+9y= | | y=5x^2+4x-2 | | 2x+5=12x | | 6+25x=20x+7 | | 2x-10-5x+15=0 | | 10x-7=4x+85 | | 9(3+2x)=-1 | | 5(x^2-3)=110 |

Equations solver categories