2x^2+54x=18

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Solution for 2x^2+54x=18 equation:


Simplifying
2x2 + 54x = 18

Reorder the terms:
54x + 2x2 = 18

Solving
54x + 2x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 54x + 2x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 54x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 27x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + 27x + x2)' equal to zero and attempt to solve: Simplifying -9 + 27x + x2 = 0 Solving -9 + 27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 27x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 27x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 27x + x2 = 0 + 9 27x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 27x + x2 = 9 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = 9 + 182.25 Reorder the terms: 182.25 + 27x + x2 = 9 + 182.25 Combine like terms: 9 + 182.25 = 191.25 182.25 + 27x + x2 = 191.25 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = 191.25 Calculate the square root of the right side: 13.829316686 Break this problem into two subproblems by setting (x + 13.5) equal to 13.829316686 and -13.829316686.

Subproblem 1

x + 13.5 = 13.829316686 Simplifying x + 13.5 = 13.829316686 Reorder the terms: 13.5 + x = 13.829316686 Solving 13.5 + x = 13.829316686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 13.829316686 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 13.829316686 + -13.5 x = 13.829316686 + -13.5 Combine like terms: 13.829316686 + -13.5 = 0.329316686 x = 0.329316686 Simplifying x = 0.329316686

Subproblem 2

x + 13.5 = -13.829316686 Simplifying x + 13.5 = -13.829316686 Reorder the terms: 13.5 + x = -13.829316686 Solving 13.5 + x = -13.829316686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -13.829316686 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -13.829316686 + -13.5 x = -13.829316686 + -13.5 Combine like terms: -13.829316686 + -13.5 = -27.329316686 x = -27.329316686 Simplifying x = -27.329316686

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.329316686, -27.329316686}

Solution

x = {0.329316686, -27.329316686}

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