-7x(x+7)=24

Simple and best practice solution for -7x(x+7)=24 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(x+7)=24 equation: 


Simplifying
-7x(x + 7) = 24

Reorder the terms:
-7x(7 + x) = 24
(7 * -7x + x * -7x) = 24
(-49x + -7x2) = 24

Solving
-49x + -7x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -49x + -7x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -49x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 49x + 7x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(24 + 49x + 7x2)' equal to zero and attempt to solve:

Simplifying
24 + 49x + 7x2 = 0

Solving
24 + 49x + 7x2 = 0

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
3.428571429 + 7x + x2 = 0

Move the constant term to the right:

Add '-3.428571429' to each side of the equation.
3.428571429 + 7x + -3.428571429 + x2 = 0 + -3.428571429

Reorder the terms:
3.428571429 + -3.428571429 + 7x + x2 = 0 + -3.428571429

Combine like terms: 3.428571429 + -3.428571429 = 0.000000000
0.000000000 + 7x + x2 = 0 + -3.428571429
7x + x2 = 0 + -3.428571429

Combine like terms: 0 + -3.428571429 = -3.428571429
7x + x2 = -3.428571429

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -3.428571429 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3.428571429 + 12.25

Combine like terms: -3.428571429 + 12.25 = 8.821428571
12.25 + 7x + x2 = 8.821428571

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 8.821428571

Calculate the square root of the right side: 2.970088984

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.970088984 and -2.970088984.


Subproblem 1
x + 3.5 = 2.970088984

Simplifying
x + 3.5 = 2.970088984

Reorder the terms:
3.5 + x = 2.970088984

Solving
3.5 + x = 2.970088984

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 2.970088984 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 2.970088984 + -3.5
x = 2.970088984 + -3.5

Combine like terms: 2.970088984 + -3.5 = -0.529911016
x = -0.529911016

Simplifying
x = -0.529911016


Subproblem 2
x + 3.5 = -2.970088984

Simplifying
x + 3.5 = -2.970088984

Reorder the terms:
3.5 + x = -2.970088984

Solving
3.5 + x = -2.970088984

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -2.970088984 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -2.970088984 + -3.5
x = -2.970088984 + -3.5

Combine like terms: -2.970088984 + -3.5 = -6.470088984
x = -6.470088984

Simplifying
x = -6.470088984


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.529911016, -6.470088984}
Solution
x = {-0.529911016, -6.470088984}

See similar equations:

| 3n-6+18=9 | | (4M-11n)(3m-2n)=0 | | 2b^2=200 | | 4(-8x+5)=-30-26 | | N/12=-10 | | 3w^2-14= | | h=5t^2+10t | | H=16t^2+8t+12 | | X*X+6X=16 | | x^3(x+2)=0 | | 20h-1.50=19.50 | | 18=3(y-63) | | 9(x-3)-(8x+6)=-6 | | 8x-3=10+3x | | -11z+11=-13-7z | | 5(2n+2)=2(4n+4) | | 2x^2+3x+8x+12=0 | | -6u-11+10u=a+2u | | 5x+8+4=6 | | 14x^2+12x=87 | | 9w-128=7w | | 3(x-4)-6=3(-2x-x)+20 | | c/2-8=6 | | 14x^2+12x=65 | | g+319-20= -2 | | 5+-1.5y=7 | | 34n+5=23n+6 | | 29(v+880)=116 | | 4j+7=91 | | 7+9=n | | 5(c-86)=40 | | 2(-3x+14)=6 |

Equations solver categories