3x(x+2)=66

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Solution for 3x(x+2)=66 equation:


Simplifying
3x(x + 2) = 66

Reorder the terms:
3x(2 + x) = 66
(2 * 3x + x * 3x) = 66
(6x + 3x2) = 66

Solving
6x + 3x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + 6x + 3x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 2x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-22 + 2x + x2)' equal to zero and attempt to solve: Simplifying -22 + 2x + x2 = 0 Solving -22 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 2x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 2x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2x + x2 = 0 + 22 2x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 2x + x2 = 22 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 22 + 1 Reorder the terms: 1 + 2x + x2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + 2x + x2 = 23 Factor a perfect square on the left side: (x + 1)(x + 1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 1) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + 1 = 4.795831523 Simplifying x + 1 = 4.795831523 Reorder the terms: 1 + x = 4.795831523 Solving 1 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.795831523 + -1 x = 4.795831523 + -1 Combine like terms: 4.795831523 + -1 = 3.795831523 x = 3.795831523 Simplifying x = 3.795831523

Subproblem 2

x + 1 = -4.795831523 Simplifying x + 1 = -4.795831523 Reorder the terms: 1 + x = -4.795831523 Solving 1 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.795831523 + -1 x = -4.795831523 + -1 Combine like terms: -4.795831523 + -1 = -5.795831523 x = -5.795831523 Simplifying x = -5.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.795831523, -5.795831523}

Solution

x = {3.795831523, -5.795831523}

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