x(2x+13)-33=0

Simple and best practice solution for x(2x+13)-33=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 x(2x+13)-33=0 equation:


Simplifying
x(2x + 13) + -33 = 0

Reorder the terms:
x(13 + 2x) + -33 = 0
(13 * x + 2x * x) + -33 = 0
(13x + 2x2) + -33 = 0

Reorder the terms:
-33 + 13x + 2x2 = 0

Solving
-33 + 13x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-16.5 + 6.5x + x2 = 0

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + 6.5x + 16.5 + x2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + 6.5x + x2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + 6.5x + x2 = 0 + 16.5
6.5x + x2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
6.5x + x2 = 16.5

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 16.5 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 16.5 + 10.5625

Combine like terms: 16.5 + 10.5625 = 27.0625
10.5625 + 6.5x + x2 = 27.0625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 27.0625

Calculate the square root of the right side: 5.202163012

Break this problem into two subproblems by setting 
(x + 3.25) equal to 5.202163012 and -5.202163012.

Subproblem 1

x + 3.25 = 5.202163012 Simplifying x + 3.25 = 5.202163012 Reorder the terms: 3.25 + x = 5.202163012 Solving 3.25 + x = 5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 5.202163012 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.202163012 + -3.25 x = 5.202163012 + -3.25 Combine like terms: 5.202163012 + -3.25 = 1.952163012 x = 1.952163012 Simplifying x = 1.952163012

Subproblem 2

x + 3.25 = -5.202163012 Simplifying x + 3.25 = -5.202163012 Reorder the terms: 3.25 + x = -5.202163012 Solving 3.25 + x = -5.202163012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -5.202163012 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.202163012 + -3.25 x = -5.202163012 + -3.25 Combine like terms: -5.202163012 + -3.25 = -8.452163012 x = -8.452163012 Simplifying x = -8.452163012

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.952163012, -8.452163012}

See similar equations:

| 5x+27.45=31.20 | | (12x+5)+(6x-5)= | | 3.75x+12=35.00 | | 4.50x+10=329.50 | | 5y+5y=2+20 | | 200-20= | | -10(x-9)(x-1)-10(x-2)(x-1)=0 | | -4(y-7)+3(2y-1)= | | -23.5=-37.7 | | (10x+22)+(7x+34)= | | y+8.5=17.2whatisy | | 23x-3y=10 | | .04t=.76 | | -56=-7k^3 | | -3(3m-3)-3m=45 | | 3x-7=5x-9-x | | 2u=-30 | | 5x+51=7x | | 8p+13=2p-5 | | 5=a/4+9 | | A=9y+3yz | | .2x=68 | | -3(x+1)=-(3x+1)+1 | | -4-8m=116 | | 4(x-8)(x+8)+4(x+8)=0 | | 6(7+9)-5x=6(5+4) | | 5z+6-2z= | | 7+x/6=-1 | | 5b^2+31b=28 | | 135=5k^3 | | .66x-4=-2 | | -2-3x=-23 |

Equations solver categories