5x(3-x)+12=

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Solution for 5x(3-x)+12= equation:


Simplifying
5x(3 + -1x) + 12 = 0
(3 * 5x + -1x * 5x) + 12 = 0
(15x + -5x2) + 12 = 0

Reorder the terms:
12 + 15x + -5x2 = 0

Solving
12 + 15x + -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 + -3x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + -3x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + -3x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + -3x + x2 = 0 + 2.4
-3x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
-3x + x2 = 2.4

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 2.4 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 2.4 + 2.25

Combine like terms: 2.4 + 2.25 = 4.65
2.25 + -3x + x2 = 4.65

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 4.65

Calculate the square root of the right side: 2.156385865

Break this problem into two subproblems by setting 
(x + -1.5) equal to 2.156385865 and -2.156385865.

Subproblem 1

x + -1.5 = 2.156385865 Simplifying x + -1.5 = 2.156385865 Reorder the terms: -1.5 + x = 2.156385865 Solving -1.5 + x = 2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.156385865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.156385865 + 1.5 x = 2.156385865 + 1.5 Combine like terms: 2.156385865 + 1.5 = 3.656385865 x = 3.656385865 Simplifying x = 3.656385865

Subproblem 2

x + -1.5 = -2.156385865 Simplifying x + -1.5 = -2.156385865 Reorder the terms: -1.5 + x = -2.156385865 Solving -1.5 + x = -2.156385865 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.156385865 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.156385865 + 1.5 x = -2.156385865 + 1.5 Combine like terms: -2.156385865 + 1.5 = -0.656385865 x = -0.656385865 Simplifying x = -0.656385865

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.656385865, -0.656385865}

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