2.4-24x=x^2

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Solution for 2.4-24x=x^2 equation:


Simplifying
2.4 + -24x = x2

Solving
2.4 + -24x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
2.4 + -24x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2.4 + 24x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 24x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 24x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 24x + x2 = 0 + 2.4
24x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
24x + x2 = 2.4

The x term is 24x.  Take half its coefficient (12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
24x + 144 + x2 = 2.4 + 144

Reorder the terms:
144 + 24x + x2 = 2.4 + 144

Combine like terms: 2.4 + 144 = 146.4
144 + 24x + x2 = 146.4

Factor a perfect square on the left side:
(x + 12)(x + 12) = 146.4

Calculate the square root of the right side: 12.09958677

Break this problem into two subproblems by setting 
(x + 12) equal to 12.09958677 and -12.09958677.

Subproblem 1

x + 12 = 12.09958677 Simplifying x + 12 = 12.09958677 Reorder the terms: 12 + x = 12.09958677 Solving 12 + x = 12.09958677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 12.09958677 + -12 Combine like terms: 12 + -12 = 0 0 + x = 12.09958677 + -12 x = 12.09958677 + -12 Combine like terms: 12.09958677 + -12 = 0.09958677 x = 0.09958677 Simplifying x = 0.09958677

Subproblem 2

x + 12 = -12.09958677 Simplifying x + 12 = -12.09958677 Reorder the terms: 12 + x = -12.09958677 Solving 12 + x = -12.09958677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -12.09958677 + -12 Combine like terms: 12 + -12 = 0 0 + x = -12.09958677 + -12 x = -12.09958677 + -12 Combine like terms: -12.09958677 + -12 = -24.09958677 x = -24.09958677 Simplifying x = -24.09958677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.09958677, -24.09958677}

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