72x(3x-78)+42x(x)=721

Simple and best practice solution for 72x(3x-78)+42x(x)=721 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 72x(3x-78)+42x(x)=721 equation:


Simplifying
72x(3x + -78) + 42x(x) = 721

Reorder the terms:
72x(-78 + 3x) + 42x(x) = 721
(-78 * 72x + 3x * 72x) + 42x(x) = 721
(-5616x + 216x2) + 42x(x) = 721

Multiply x * x
-5616x + 216x2 + 42x2 = 721

Combine like terms: 216x2 + 42x2 = 258x2
-5616x + 258x2 = 721

Solving
-5616x + 258x2 = 721

Solving for variable 'x'.

Reorder the terms:
-721 + -5616x + 258x2 = 721 + -721

Combine like terms: 721 + -721 = 0
-721 + -5616x + 258x2 = 0

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

Divide each side by '258'.
-2.794573643 + -21.76744186x + x2 = 0

Move the constant term to the right:

Add '2.794573643' to each side of the equation.
-2.794573643 + -21.76744186x + 2.794573643 + x2 = 0 + 2.794573643

Reorder the terms:
-2.794573643 + 2.794573643 + -21.76744186x + x2 = 0 + 2.794573643

Combine like terms: -2.794573643 + 2.794573643 = 0.000000000
0.000000000 + -21.76744186x + x2 = 0 + 2.794573643
-21.76744186x + x2 = 0 + 2.794573643

Combine like terms: 0 + 2.794573643 = 2.794573643
-21.76744186x + x2 = 2.794573643

The x term is -21.76744186x.  Take half its coefficient (-10.88372093).
Square it (118.4553813) and add it to both sides.

Add '118.4553813' to each side of the equation.
-21.76744186x + 118.4553813 + x2 = 2.794573643 + 118.4553813

Reorder the terms:
118.4553813 + -21.76744186x + x2 = 2.794573643 + 118.4553813

Combine like terms: 2.794573643 + 118.4553813 = 121.249954943
118.4553813 + -21.76744186x + x2 = 121.249954943

Factor a perfect square on the left side:
(x + -10.88372093)(x + -10.88372093) = 121.249954943

Calculate the square root of the right side: 11.011355727

Break this problem into two subproblems by setting 
(x + -10.88372093) equal to 11.011355727 and -11.011355727.

Subproblem 1

x + -10.88372093 = 11.011355727 Simplifying x + -10.88372093 = 11.011355727 Reorder the terms: -10.88372093 + x = 11.011355727 Solving -10.88372093 + x = 11.011355727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.88372093' to each side of the equation. -10.88372093 + 10.88372093 + x = 11.011355727 + 10.88372093 Combine like terms: -10.88372093 + 10.88372093 = 0.00000000 0.00000000 + x = 11.011355727 + 10.88372093 x = 11.011355727 + 10.88372093 Combine like terms: 11.011355727 + 10.88372093 = 21.895076657 x = 21.895076657 Simplifying x = 21.895076657

Subproblem 2

x + -10.88372093 = -11.011355727 Simplifying x + -10.88372093 = -11.011355727 Reorder the terms: -10.88372093 + x = -11.011355727 Solving -10.88372093 + x = -11.011355727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.88372093' to each side of the equation. -10.88372093 + 10.88372093 + x = -11.011355727 + 10.88372093 Combine like terms: -10.88372093 + 10.88372093 = 0.00000000 0.00000000 + x = -11.011355727 + 10.88372093 x = -11.011355727 + 10.88372093 Combine like terms: -11.011355727 + 10.88372093 = -0.127634797 x = -0.127634797 Simplifying x = -0.127634797

Solution

The solution to the problem is based on the solutions from the subproblems. x = {21.895076657, -0.127634797}

See similar equations:

| 95=5*c | | 246=2 | | 5(x-7)+9=104 | | 8=88*j | | M*5=90 | | 124=l*4 | | 19-3x+2y=27 | | 8+12-s=5 | | 24-17=s | | 46-p=33 | | 8-7=b | | 19-4-11=b | | 8+12-12=0 | | T*6=30 | | 15-f=13 | | 90*p=3*3 | | 15+9+3+c=41 | | 9c-11=70 | | 4t+3=15 | | 5x-1=-4 | | 4(-8+-3x^3+x^4)=0 | | 4x^4-12x^3-32=0 | | 4x^4-12x^3-32= | | 46-p=3*3 | | 46-p=3*11 | | 10x+7=14x-5 | | 7*x^2+2*x=0 | | 7*x^2+2*x=m | | x^2-10*x+119=0 | | 8a+2=18 | | 8a+2=10 | | (20-2m)=(m-130) |

Equations solver categories