0=3x^2-3x-729

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Solution for 0=3x^2-3x-729 equation:


Simplifying
0 = 3x2 + -3x + -729

Reorder the terms:
0 = -729 + -3x + 3x2

Solving
0 = -729 + -3x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 729 = 729
729 + 3x + -3x2 = -729 + -3x + 3x2 + 729 + 3x + -3x2

Reorder the terms:
729 + 3x + -3x2 = -729 + 729 + -3x + 3x + 3x2 + -3x2

Combine like terms: -729 + 729 = 0
729 + 3x + -3x2 = 0 + -3x + 3x + 3x2 + -3x2
729 + 3x + -3x2 = -3x + 3x + 3x2 + -3x2

Combine like terms: -3x + 3x = 0
729 + 3x + -3x2 = 0 + 3x2 + -3x2
729 + 3x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
729 + 3x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(243 + x + -1x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(243 + x + -1x2)' equal to zero and attempt to solve: Simplifying 243 + x + -1x2 = 0 Solving 243 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -243 + -1x + x2 = 0 Move the constant term to the right: Add '243' to each side of the equation. -243 + -1x + 243 + x2 = 0 + 243 Reorder the terms: -243 + 243 + -1x + x2 = 0 + 243 Combine like terms: -243 + 243 = 0 0 + -1x + x2 = 0 + 243 -1x + x2 = 0 + 243 Combine like terms: 0 + 243 = 243 -1x + x2 = 243 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 243 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 243 + 0.25 Combine like terms: 243 + 0.25 = 243.25 0.25 + -1x + x2 = 243.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 243.25 Calculate the square root of the right side: 15.59647396 Break this problem into two subproblems by setting (x + 0.5) equal to 15.59647396 and -15.59647396.

Subproblem 1

x + 0.5 = 15.59647396 Simplifying x + 0.5 = 15.59647396 Reorder the terms: 0.5 + x = 15.59647396 Solving 0.5 + x = 15.59647396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 15.59647396 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 15.59647396 + -0.5 x = 15.59647396 + -0.5 Combine like terms: 15.59647396 + -0.5 = 15.09647396 x = 15.09647396 Simplifying x = 15.09647396

Subproblem 2

x + 0.5 = -15.59647396 Simplifying x + 0.5 = -15.59647396 Reorder the terms: 0.5 + x = -15.59647396 Solving 0.5 + x = -15.59647396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -15.59647396 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -15.59647396 + -0.5 x = -15.59647396 + -0.5 Combine like terms: -15.59647396 + -0.5 = -16.09647396 x = -16.09647396 Simplifying x = -16.09647396

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.09647396, -16.09647396}

Solution

x = {15.09647396, -16.09647396}

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