5x^2-24x+12=

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Solution for 5x^2-24x+12= equation:


Simplifying
5x2 + -24x + 12 = 0

Reorder the terms:
12 + -24x + 5x2 = 0

Solving
12 + -24x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
2.4 + -4.8x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -4.8x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -4.8x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -4.8x + x2 = 0 + -2.4
-4.8x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-4.8x + x2 = -2.4

The x term is -4.8x.  Take half its coefficient (-2.4).
Square it (5.76) and add it to both sides.

Add '5.76' to each side of the equation.
-4.8x + 5.76 + x2 = -2.4 + 5.76

Reorder the terms:
5.76 + -4.8x + x2 = -2.4 + 5.76

Combine like terms: -2.4 + 5.76 = 3.36
5.76 + -4.8x + x2 = 3.36

Factor a perfect square on the left side:
(x + -2.4)(x + -2.4) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(x + -2.4) equal to 1.833030278 and -1.833030278.

Subproblem 1

x + -2.4 = 1.833030278 Simplifying x + -2.4 = 1.833030278 Reorder the terms: -2.4 + x = 1.833030278 Solving -2.4 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 1.833030278 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 1.833030278 + 2.4 x = 1.833030278 + 2.4 Combine like terms: 1.833030278 + 2.4 = 4.233030278 x = 4.233030278 Simplifying x = 4.233030278

Subproblem 2

x + -2.4 = -1.833030278 Simplifying x + -2.4 = -1.833030278 Reorder the terms: -2.4 + x = -1.833030278 Solving -2.4 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -1.833030278 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -1.833030278 + 2.4 x = -1.833030278 + 2.4 Combine like terms: -1.833030278 + 2.4 = 0.566969722 x = 0.566969722 Simplifying x = 0.566969722

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.233030278, 0.566969722}

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