3x(x+18)=246

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Solution for 3x(x+18)=246 equation:


Simplifying
3x(x + 18) = 246

Reorder the terms:
3x(18 + x) = 246
(18 * 3x + x * 3x) = 246
(54x + 3x2) = 246

Solving
54x + 3x2 = 246

Solving for variable 'x'.

Reorder the terms:
-246 + 54x + 3x2 = 246 + -246

Combine like terms: 246 + -246 = 0
-246 + 54x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-82 + 18x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-82 + 18x + x2)' equal to zero and attempt to solve: Simplifying -82 + 18x + x2 = 0 Solving -82 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '82' to each side of the equation. -82 + 18x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 18x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 18x + x2 = 0 + 82 18x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 18x + x2 = 82 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = 82 + 81 Reorder the terms: 81 + 18x + x2 = 82 + 81 Combine like terms: 82 + 81 = 163 81 + 18x + x2 = 163 Factor a perfect square on the left side: (x + 9)(x + 9) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 9) equal to 12.767145335 and -12.767145335.

Subproblem 1

x + 9 = 12.767145335 Simplifying x + 9 = 12.767145335 Reorder the terms: 9 + x = 12.767145335 Solving 9 + x = 12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 12.767145335 + -9 Combine like terms: 9 + -9 = 0 0 + x = 12.767145335 + -9 x = 12.767145335 + -9 Combine like terms: 12.767145335 + -9 = 3.767145335 x = 3.767145335 Simplifying x = 3.767145335

Subproblem 2

x + 9 = -12.767145335 Simplifying x + 9 = -12.767145335 Reorder the terms: 9 + x = -12.767145335 Solving 9 + x = -12.767145335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -12.767145335 + -9 Combine like terms: 9 + -9 = 0 0 + x = -12.767145335 + -9 x = -12.767145335 + -9 Combine like terms: -12.767145335 + -9 = -21.767145335 x = -21.767145335 Simplifying x = -21.767145335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.767145335, -21.767145335}

Solution

x = {3.767145335, -21.767145335}

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