24x(45x-67)=23

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Solution for 24x(45x-67)=23 equation:


Simplifying
24x(45x + -67) = 23

Reorder the terms:
24x(-67 + 45x) = 23
(-67 * 24x + 45x * 24x) = 23
(-1608x + 1080x2) = 23

Solving
-1608x + 1080x2 = 23

Solving for variable 'x'.

Reorder the terms:
-23 + -1608x + 1080x2 = 23 + -23

Combine like terms: 23 + -23 = 0
-23 + -1608x + 1080x2 = 0

Begin completing the square.  Divide all terms by
1080 the coefficient of the squared term: 

Divide each side by '1080'.
-0.0212962963 + -1.488888889x + x2 = 0.0

Move the constant term to the right:

Add '0.0212962963' to each side of the equation.
-0.0212962963 + -1.488888889x + 0.0212962963 + x2 = 0.0 + 0.0212962963

Reorder the terms:
-0.0212962963 + 0.0212962963 + -1.488888889x + x2 = 0.0 + 0.0212962963

Combine like terms: -0.0212962963 + 0.0212962963 = 0.0000000000
0.0000000000 + -1.488888889x + x2 = 0.0 + 0.0212962963
-1.488888889x + x2 = 0.0 + 0.0212962963

Combine like terms: 0.0 + 0.0212962963 = 0.0212962963
-1.488888889x + x2 = 0.0212962963

The x term is -1.488888889x.  Take half its coefficient (-0.7444444445).
Square it (0.5541975309) and add it to both sides.

Add '0.5541975309' to each side of the equation.
-1.488888889x + 0.5541975309 + x2 = 0.0212962963 + 0.5541975309

Reorder the terms:
0.5541975309 + -1.488888889x + x2 = 0.0212962963 + 0.5541975309

Combine like terms: 0.0212962963 + 0.5541975309 = 0.5754938272
0.5541975309 + -1.488888889x + x2 = 0.5754938272

Factor a perfect square on the left side:
(x + -0.7444444445)(x + -0.7444444445) = 0.5754938272

Calculate the square root of the right side: 0.758613095

Break this problem into two subproblems by setting 
(x + -0.7444444445) equal to 0.758613095 and -0.758613095.

Subproblem 1

x + -0.7444444445 = 0.758613095 Simplifying x + -0.7444444445 = 0.758613095 Reorder the terms: -0.7444444445 + x = 0.758613095 Solving -0.7444444445 + x = 0.758613095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7444444445' to each side of the equation. -0.7444444445 + 0.7444444445 + x = 0.758613095 + 0.7444444445 Combine like terms: -0.7444444445 + 0.7444444445 = 0.0000000000 0.0000000000 + x = 0.758613095 + 0.7444444445 x = 0.758613095 + 0.7444444445 Combine like terms: 0.758613095 + 0.7444444445 = 1.5030575395 x = 1.5030575395 Simplifying x = 1.5030575395

Subproblem 2

x + -0.7444444445 = -0.758613095 Simplifying x + -0.7444444445 = -0.758613095 Reorder the terms: -0.7444444445 + x = -0.758613095 Solving -0.7444444445 + x = -0.758613095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7444444445' to each side of the equation. -0.7444444445 + 0.7444444445 + x = -0.758613095 + 0.7444444445 Combine like terms: -0.7444444445 + 0.7444444445 = 0.0000000000 0.0000000000 + x = -0.758613095 + 0.7444444445 x = -0.758613095 + 0.7444444445 Combine like terms: -0.758613095 + 0.7444444445 = -0.0141686505 x = -0.0141686505 Simplifying x = -0.0141686505

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.5030575395, -0.0141686505}

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