3x^2-3x=84

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Solution for 3x^2-3x=84 equation:


Simplifying
3x2 + -3x = 84

Reorder the terms:
-3x + 3x2 = 84

Solving
-3x + 3x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -3x + 3x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -1x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-28 + -1x + x2)' equal to zero and attempt to solve: Simplifying -28 + -1x + x2 = 0 Solving -28 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -1x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -1x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -1x + x2 = 0 + 28 -1x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -1x + x2 = 28 The x term is -1x. 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 = 28 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + -1x + x2 = 28.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -0.5) equal to 5.315072906 and -5.315072906.

Subproblem 1

x + -0.5 = 5.315072906 Simplifying x + -0.5 = 5.315072906 Reorder the terms: -0.5 + x = 5.315072906 Solving -0.5 + x = 5.315072906 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 = 5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.315072906 + 0.5 x = 5.315072906 + 0.5 Combine like terms: 5.315072906 + 0.5 = 5.815072906 x = 5.815072906 Simplifying x = 5.815072906

Subproblem 2

x + -0.5 = -5.315072906 Simplifying x + -0.5 = -5.315072906 Reorder the terms: -0.5 + x = -5.315072906 Solving -0.5 + x = -5.315072906 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 = -5.315072906 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.315072906 + 0.5 x = -5.315072906 + 0.5 Combine like terms: -5.315072906 + 0.5 = -4.815072906 x = -4.815072906 Simplifying x = -4.815072906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.815072906, -4.815072906}

Solution

x = {5.815072906, -4.815072906}

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