3((x+2)(x+2))-4=11

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Solution for 3((x+2)(x+2))-4=11 equation:


Simplifying
3((x + 2)(x + 2)) + -4 = 11

Reorder the terms:
3((2 + x)(x + 2)) + -4 = 11

Reorder the terms:
3((2 + x)(2 + x)) + -4 = 11

Multiply (2 + x) * (2 + x)
3((2(2 + x) + x(2 + x))) + -4 = 11
3(((2 * 2 + x * 2) + x(2 + x))) + -4 = 11
3(((4 + 2x) + x(2 + x))) + -4 = 11
3((4 + 2x + (2 * x + x * x))) + -4 = 11
3((4 + 2x + (2x + x2))) + -4 = 11

Combine like terms: 2x + 2x = 4x
3((4 + 4x + x2)) + -4 = 11
(4 * 3 + 4x * 3 + x2 * 3) + -4 = 11
(12 + 12x + 3x2) + -4 = 11

Reorder the terms:
12 + -4 + 12x + 3x2 = 11

Combine like terms: 12 + -4 = 8
8 + 12x + 3x2 = 11

Solving
8 + 12x + 3x2 = 11

Solving for variable 'x'.

Reorder the terms:
8 + -11 + 12x + 3x2 = 11 + -11

Combine like terms: 8 + -11 = -3
-3 + 12x + 3x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-3 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 1

x + 2 = 2.236067978 Simplifying x + 2 = 2.236067978 Reorder the terms: 2 + x = 2.236067978 Solving 2 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.236067978 + -2 x = 2.236067978 + -2 Combine like terms: 2.236067978 + -2 = 0.236067978 x = 0.236067978 Simplifying x = 0.236067978

Subproblem 2

x + 2 = -2.236067978 Simplifying x + 2 = -2.236067978 Reorder the terms: 2 + x = -2.236067978 Solving 2 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.236067978 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.236067978 + -2 x = -2.236067978 + -2 Combine like terms: -2.236067978 + -2 = -4.236067978 x = -4.236067978 Simplifying x = -4.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.236067978, -4.236067978}

Solution

x = {0.236067978, -4.236067978}

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