(3x)(3x+1)=98

Simple and best practice solution for (3x)(3x+1)=98 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 (3x)(3x+1)=98 equation:


Simplifying
(3x)(3x + 1) = 98

Remove parenthesis around (3x)
3x(3x + 1) = 98

Reorder the terms:
3x(1 + 3x) = 98
(1 * 3x + 3x * 3x) = 98
(3x + 9x2) = 98

Solving
3x + 9x2 = 98

Solving for variable 'x'.

Reorder the terms:
-98 + 3x + 9x2 = 98 + -98

Combine like terms: 98 + -98 = 0
-98 + 3x + 9x2 = 0

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

Divide each side by '9'.
-10.88888889 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '10.88888889' to each side of the equation.
-10.88888889 + 0.3333333333x + 10.88888889 + x2 = 0 + 10.88888889

Reorder the terms:
-10.88888889 + 10.88888889 + 0.3333333333x + x2 = 0 + 10.88888889

Combine like terms: -10.88888889 + 10.88888889 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 10.88888889
0.3333333333x + x2 = 0 + 10.88888889

Combine like terms: 0 + 10.88888889 = 10.88888889
0.3333333333x + x2 = 10.88888889

The x term is 0.3333333333x.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333x + 0.02777777779 + x2 = 10.88888889 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333x + x2 = 10.88888889 + 0.02777777779

Combine like terms: 10.88888889 + 0.02777777779 = 10.91666666779
0.02777777779 + 0.3333333333x + x2 = 10.91666666779

Factor a perfect square on the left side:
(x + 0.1666666667)(x + 0.1666666667) = 10.91666666779

Calculate the square root of the right side: 3.304037934

Break this problem into two subproblems by setting 
(x + 0.1666666667) equal to 3.304037934 and -3.304037934.

Subproblem 1

x + 0.1666666667 = 3.304037934 Simplifying x + 0.1666666667 = 3.304037934 Reorder the terms: 0.1666666667 + x = 3.304037934 Solving 0.1666666667 + x = 3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 3.304037934 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 3.304037934 + -0.1666666667 x = 3.304037934 + -0.1666666667 Combine like terms: 3.304037934 + -0.1666666667 = 3.1373712673 x = 3.1373712673 Simplifying x = 3.1373712673

Subproblem 2

x + 0.1666666667 = -3.304037934 Simplifying x + 0.1666666667 = -3.304037934 Reorder the terms: 0.1666666667 + x = -3.304037934 Solving 0.1666666667 + x = -3.304037934 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -3.304037934 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -3.304037934 + -0.1666666667 x = -3.304037934 + -0.1666666667 Combine like terms: -3.304037934 + -0.1666666667 = -3.4707046007 x = -3.4707046007 Simplifying x = -3.4707046007

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.1373712673, -3.4707046007}

See similar equations:

| 5y=3y^2-8 | | x/4-1/3=5/12 | | 6x+5+8x=75 | | F(x)=-x^4+3x^3+2x^2-5x-4 | | y(y-16)=5/3 | | 27=4x-17 | | 5y^3-126y=9y^22 | | x+6+3x-22=36 | | 63/100 | | 3ysquare+4y+1=0 | | 1500=(1500/t)-10t-50 | | 20x+-1+3x=22 | | 11+3x-20=13+x | | 18x-26=9x+38 | | 1500=1500/t-10t-50 | | 4x^5-5x^4+1=0 | | 2+2x+5=5x-8 | | 5sin(3x)=4 | | L-6=2w | | 1/3=x-1/4 | | 5y^3-126=9y^2 | | 12+3x-5=44 | | 3k-3.5=100 | | 8+3x-16=2x+3 | | 4(x+3)+3(2x-3)=53 | | 5x-8=2+5x-10 | | 4y-3x=-1 | | K/3=k-1/5 | | 2x+28+14=x+31 | | 23x=78-4x | | x+(x+2)+(x+4)=288 | | 2.5*3.14= |

Equations solver categories