3x(x+2)+4=16

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Solution for 3x(x+2)+4=16 equation:


Simplifying
3x(x + 2) + 4 = 16

Reorder the terms:
3x(2 + x) + 4 = 16
(2 * 3x + x * 3x) + 4 = 16
(6x + 3x2) + 4 = 16

Reorder the terms:
4 + 6x + 3x2 = 16

Solving
4 + 6x + 3x2 = 16

Solving for variable 'x'.

Reorder the terms:
4 + -16 + 6x + 3x2 = 16 + -16

Combine like terms: 4 + -16 = -12
-12 + 6x + 3x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-12 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 2x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + 2x + x2)' equal to zero and attempt to solve: Simplifying -4 + 2x + x2 = 0 Solving -4 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 2x + x2 = 0 + 4 2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 2x + x2 = 4 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 = 4 + 1 Reorder the terms: 1 + 2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + 2x + x2 = 5 Factor a perfect square on the left side: (x + 1)(x + 1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 1) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + 1 = 2.236067978 Simplifying x + 1 = 2.236067978 Reorder the terms: 1 + x = 2.236067978 Solving 1 + x = 2.236067978 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 = 2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.236067978 + -1 x = 2.236067978 + -1 Combine like terms: 2.236067978 + -1 = 1.236067978 x = 1.236067978 Simplifying x = 1.236067978

Subproblem 2

x + 1 = -2.236067978 Simplifying x + 1 = -2.236067978 Reorder the terms: 1 + x = -2.236067978 Solving 1 + x = -2.236067978 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 = -2.236067978 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.236067978 + -1 x = -2.236067978 + -1 Combine like terms: -2.236067978 + -1 = -3.236067978 x = -3.236067978 Simplifying x = -3.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.236067978, -3.236067978}

Solution

x = {1.236067978, -3.236067978}

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