2(x+1)(x+1)=12

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Solution for 2(x+1)(x+1)=12 equation:


Simplifying
2(x + 1)(x + 1) = 12

Reorder the terms:
2(1 + x)(x + 1) = 12

Reorder the terms:
2(1 + x)(1 + x) = 12

Multiply (1 + x) * (1 + x)
2(1(1 + x) + x(1 + x)) = 12
2((1 * 1 + x * 1) + x(1 + x)) = 12
2((1 + 1x) + x(1 + x)) = 12
2(1 + 1x + (1 * x + x * x)) = 12
2(1 + 1x + (1x + x2)) = 12

Combine like terms: 1x + 1x = 2x
2(1 + 2x + x2) = 12
(1 * 2 + 2x * 2 + x2 * 2) = 12
(2 + 4x + 2x2) = 12

Solving
2 + 4x + 2x2 = 12

Solving for variable 'x'.

Reorder the terms:
2 + -12 + 4x + 2x2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + 4x + 2x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + 2x + x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + x2 = 0 Solving -5 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x + x2 = 0 + 5 2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2x + x2 = 5 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 = 5 + 1 Reorder the terms: 1 + 2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x + x2 = 6 Factor a perfect square on the left side: (x + 1)(x + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 1) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + 1 = 2.449489743 Simplifying x + 1 = 2.449489743 Reorder the terms: 1 + x = 2.449489743 Solving 1 + x = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.449489743 + -1 x = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x = 1.449489743 Simplifying x = 1.449489743

Subproblem 2

x + 1 = -2.449489743 Simplifying x + 1 = -2.449489743 Reorder the terms: 1 + x = -2.449489743 Solving 1 + x = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.449489743 + -1 x = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x = -3.449489743 Simplifying x = -3.449489743

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.449489743, -3.449489743}

Solution

x = {1.449489743, -3.449489743}

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