7x-12x^3-(4x^2)=0

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Solution for 7x-12x^3-(4x^2)=0 equation:


Simplifying
7x + -12x3 + -1(4x2) = 0

Remove parenthesis around (4x2)
7x + -12x3 + -1 * 4x2 = 0

Multiply -1 * 4
7x + -12x3 + -4x2 = 0

Reorder the terms:
7x + -4x2 + -12x3 = 0

Solving
7x + -4x2 + -12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + -4x + -12x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(7 + -4x + -12x2)' equal to zero and attempt to solve: Simplifying 7 + -4x + -12x2 = 0 Solving 7 + -4x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5833333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + 0.3333333333x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + 0.3333333333x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.5833333333 0.3333333333x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 0.3333333333x + x2 = 0.5833333333 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.5833333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.5833333333 + 0.02777777779 Combine like terms: 0.5833333333 + 0.02777777779 = 0.61111111109 0.02777777779 + 0.3333333333x + x2 = 0.61111111109 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.61111111109 Calculate the square root of the right side: 0.78173596 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.78173596 and -0.78173596.

Subproblem 1

x + 0.1666666667 = 0.78173596 Simplifying x + 0.1666666667 = 0.78173596 Reorder the terms: 0.1666666667 + x = 0.78173596 Solving 0.1666666667 + x = 0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.78173596 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.78173596 + -0.1666666667 x = 0.78173596 + -0.1666666667 Combine like terms: 0.78173596 + -0.1666666667 = 0.6150692933 x = 0.6150692933 Simplifying x = 0.6150692933

Subproblem 2

x + 0.1666666667 = -0.78173596 Simplifying x + 0.1666666667 = -0.78173596 Reorder the terms: 0.1666666667 + x = -0.78173596 Solving 0.1666666667 + x = -0.78173596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.78173596 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.78173596 + -0.1666666667 x = -0.78173596 + -0.1666666667 Combine like terms: -0.78173596 + -0.1666666667 = -0.9484026267 x = -0.9484026267 Simplifying x = -0.9484026267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6150692933, -0.9484026267}

Solution

x = {0, 0.6150692933, -0.9484026267}

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