x(2x-3)=13

Simple and best practice solution for x(2x-3)=13 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-3)=13 equation: 


Simplifying
x(2x + -3) = 13

Reorder the terms:
x(-3 + 2x) = 13
(-3 * x + 2x * x) = 13
(-3x + 2x2) = 13

Solving
-3x + 2x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + -3x + 2x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + -3x + 2x2 = 0

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

Divide each side by '2'.
-6.5 + -1.5x + x2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + -1.5x + 6.5 + x2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + -1.5x + x2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + -1.5x + x2 = 0 + 6.5
-1.5x + x2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
-1.5x + x2 = 6.5

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 6.5 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 6.5 + 0.5625

Combine like terms: 6.5 + 0.5625 = 7.0625
0.5625 + -1.5x + x2 = 7.0625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.657536453 and -2.657536453.


Subproblem 1
x + -0.75 = 2.657536453

Simplifying
x + -0.75 = 2.657536453

Reorder the terms:
-0.75 + x = 2.657536453

Solving
-0.75 + x = 2.657536453

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 2.657536453 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 2.657536453 + 0.75
x = 2.657536453 + 0.75

Combine like terms: 2.657536453 + 0.75 = 3.407536453
x = 3.407536453

Simplifying
x = 3.407536453


Subproblem 2
x + -0.75 = -2.657536453

Simplifying
x + -0.75 = -2.657536453

Reorder the terms:
-0.75 + x = -2.657536453

Solving
-0.75 + x = -2.657536453

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -2.657536453 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -2.657536453 + 0.75
x = -2.657536453 + 0.75

Combine like terms: -2.657536453 + 0.75 = -1.907536453
x = -1.907536453

Simplifying
x = -1.907536453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.407536453, -1.907536453}

See similar equations:

| 9.63/3 | | (-6-4)(4)= | | (-6-4)(4)/(-5)-(-10)= | | 4x^2+9y^2-1=0 | | (3)(-4)(-1)(-6)= | | -18y+7= | | =1+9x+27x^2+28x^3 | | (-45)+(-72)= | | 567/13 | | lnx=4.65895 | | Ln(x^3)+ln(x^2)=10 | | (-34)+(-23)+41= | | lny=4.65895 | | 7.8-2.1(3.6)/4 | | 1/6x3/2 | | -3B+5B+7=-4 | | x+x(5)=180 | | 96/x=100/35 | | 2000=0.25x^3 | | -2x=exp(x) | | -2x=ex | | -7=5y+4(-4+9)-7(7+3y) | | 4m+6n+8m+5n= | | x+x(5)=90 | | x=2y-11 | | 33=x | | 2sin^23x-1=0 | | 3x(4y)=12 | | 10-x=8-4x | | 3x^2+8=5 | | 2x+20=8x-4x | | -16=8/5x |

Equations solver categories