(x-3)(9x-5)=1

Simple and best practice solution for (x-3)(9x-5)=1 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-3)(9x-5)=1 equation:


Simplifying
(x + -3)(9x + -5) = 1

Reorder the terms:
(-3 + x)(9x + -5) = 1

Reorder the terms:
(-3 + x)(-5 + 9x) = 1

Multiply (-3 + x) * (-5 + 9x)
(-3(-5 + 9x) + x(-5 + 9x)) = 1
((-5 * -3 + 9x * -3) + x(-5 + 9x)) = 1
((15 + -27x) + x(-5 + 9x)) = 1
(15 + -27x + (-5 * x + 9x * x)) = 1
(15 + -27x + (-5x + 9x2)) = 1

Combine like terms: -27x + -5x = -32x
(15 + -32x + 9x2) = 1

Solving
15 + -32x + 9x2 = 1

Solving for variable 'x'.

Reorder the terms:
15 + -1 + -32x + 9x2 = 1 + -1

Combine like terms: 15 + -1 = 14
14 + -32x + 9x2 = 1 + -1

Combine like terms: 1 + -1 = 0
14 + -32x + 9x2 = 0

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

Divide each side by '9'.
1.555555556 + -3.555555556x + x2 = 0

Move the constant term to the right:

Add '-1.555555556' to each side of the equation.
1.555555556 + -3.555555556x + -1.555555556 + x2 = 0 + -1.555555556

Reorder the terms:
1.555555556 + -1.555555556 + -3.555555556x + x2 = 0 + -1.555555556

Combine like terms: 1.555555556 + -1.555555556 = 0.000000000
0.000000000 + -3.555555556x + x2 = 0 + -1.555555556
-3.555555556x + x2 = 0 + -1.555555556

Combine like terms: 0 + -1.555555556 = -1.555555556
-3.555555556x + x2 = -1.555555556

The x term is -3.555555556x.  Take half its coefficient (-1.777777778).
Square it (3.160493828) and add it to both sides.

Add '3.160493828' to each side of the equation.
-3.555555556x + 3.160493828 + x2 = -1.555555556 + 3.160493828

Reorder the terms:
3.160493828 + -3.555555556x + x2 = -1.555555556 + 3.160493828

Combine like terms: -1.555555556 + 3.160493828 = 1.604938272
3.160493828 + -3.555555556x + x2 = 1.604938272

Factor a perfect square on the left side:
(x + -1.777777778)(x + -1.777777778) = 1.604938272

Calculate the square root of the right side: 1.266861584

Break this problem into two subproblems by setting 
(x + -1.777777778) equal to 1.266861584 and -1.266861584.

Subproblem 1

x + -1.777777778 = 1.266861584 Simplifying x + -1.777777778 = 1.266861584 Reorder the terms: -1.777777778 + x = 1.266861584 Solving -1.777777778 + x = 1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = 1.266861584 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = 1.266861584 + 1.777777778 x = 1.266861584 + 1.777777778 Combine like terms: 1.266861584 + 1.777777778 = 3.044639362 x = 3.044639362 Simplifying x = 3.044639362

Subproblem 2

x + -1.777777778 = -1.266861584 Simplifying x + -1.777777778 = -1.266861584 Reorder the terms: -1.777777778 + x = -1.266861584 Solving -1.777777778 + x = -1.266861584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.777777778' to each side of the equation. -1.777777778 + 1.777777778 + x = -1.266861584 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + x = -1.266861584 + 1.777777778 x = -1.266861584 + 1.777777778 Combine like terms: -1.266861584 + 1.777777778 = 0.510916194 x = 0.510916194 Simplifying x = 0.510916194

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.044639362, 0.510916194}

See similar equations:

| -0.125c=4 | | 75/83=n/747 | | z-15=-2 | | 10-4x+5x=8 | | f(x)=10x^5 | | y=30(1)+30 | | 2.25=4 | | 16-x=-2 | | n+(n+2)+n+4=42 | | z+17=29 | | -0.25x=7 | | ln(5)-ln(4x)=5 | | 6x-14/5=2x | | y=30(1) | | 7x+1+3=21 | | y=35(1)+30 | | .375p-3=.125p-5 | | x=sin(2*3.14156) | | 108=a+b | | .4x-1=.5x+2 | | x=pi | | -2(2.5)-3y=-7 | | 4m+2m-5m-1=14 | | =9y^2+9y+2 | | x=sin(pi*2) | | .4x-1=l | | (16/6)*x=0.5 | | 6x^2+48x=12 | | x=x^2-2*x-6 | | x=x^2-2*x+6 | | 3/4x-1*3/4x-1 | | 4z+y-2z+14y= |

Equations solver categories