7(x^2-21)=49(2x)

Simple and best practice solution for 7(x^2-21)=49(2x) 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 7(x^2-21)=49(2x) equation: 


Simplifying
7(x2 + -21) = 49(2x)

Reorder the terms:
7(-21 + x2) = 49(2x)
(-21 * 7 + x2 * 7) = 49(2x)
(-147 + 7x2) = 49(2x)

Remove parenthesis around (2x)
-147 + 7x2 = 49 * 2x

Multiply 49 * 2
-147 + 7x2 = 98x

Solving
-147 + 7x2 = 98x

Solving for variable 'x'.

Reorder the terms:
-147 + -98x + 7x2 = 98x + -98x

Combine like terms: 98x + -98x = 0
-147 + -98x + 7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-21 + -14x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-21 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + -14x + x2 = 0

Solving
-21 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -14x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + -14x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -14x + x2 = 0 + 21
-14x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
-14x + x2 = 21

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 = 21 + 49

Reorder the terms:
49 + -14x + x2 = 21 + 49

Combine like terms: 21 + 49 = 70
49 + -14x + x2 = 70

Factor a perfect square on the left side:
(x + -7)(x + -7) = 70

Calculate the square root of the right side: 8.366600265

Break this problem into two subproblems by setting 
(x + -7) equal to 8.366600265 and -8.366600265.


Subproblem 1
x + -7 = 8.366600265

Simplifying
x + -7 = 8.366600265

Reorder the terms:
-7 + x = 8.366600265

Solving
-7 + x = 8.366600265

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 = 8.366600265 + 7

Combine like terms: -7 + 7 = 0
0 + x = 8.366600265 + 7
x = 8.366600265 + 7

Combine like terms: 8.366600265 + 7 = 15.366600265
x = 15.366600265

Simplifying
x = 15.366600265


Subproblem 2
x + -7 = -8.366600265

Simplifying
x + -7 = -8.366600265

Reorder the terms:
-7 + x = -8.366600265

Solving
-7 + x = -8.366600265

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 = -8.366600265 + 7

Combine like terms: -7 + 7 = 0
0 + x = -8.366600265 + 7
x = -8.366600265 + 7

Combine like terms: -8.366600265 + 7 = -1.366600265
x = -1.366600265

Simplifying
x = -1.366600265


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.366600265, -1.366600265}
Solution
x = {15.366600265, -1.366600265}

See similar equations:

| -7x+6y=10 | | 2x+13=2-3x | | AX-C+D+BX=0 | | 4x-8+2x=7x-x-8 | | -2(x-3)-5x=36 | | 25x+9y=208 | | 27a^5b^3-64a^8= | | -12w+14=8w-46 | | -13x+8x=23 | | 12+m=12 | | m-[-4]=7 | | 144x^2-16=9 | | 4x+8-x= | | 4+2(-8z-7)=(2z-9)+2 | | c^2-4c-5=0 | | -6+8z=21z-45 | | 2z+44=0 | | 5x-4+6y= | | 2(x-3)=4x+8 | | 3-4b=10b+4 | | 0=4x^4+27x^2-81 | | 85-65=2x+-7x | | x+(x+2)+(3x-5)=37 | | 8v-5=7v+12 | | 2/3+w=11/5 | | 2r+5=32r+11 | | 0=(3/2)x-5 | | 13+x=5x+1 | | 3+5(6-3)=x | | 0=(1/3)x+5 | | 12-3(y+1)=1-5(y-2) | | 2y+3z=15 |

Equations solver categories