x(x+4)+x(x+2)=2x+2

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


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

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

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

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

Combine like terms: 4x + 2x = 6x
6x + x2 + x2 = 2x + 2

Combine like terms: x2 + x2 = 2x2
6x + 2x2 = 2x + 2

Reorder the terms:
6x + 2x2 = 2 + 2x

Solving
6x + 2x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-2 + 6x + -2x + 2x2 = 2 + 2x + -2 + -2x

Combine like terms: 6x + -2x = 4x
-2 + 4x + 2x2 = 2 + 2x + -2 + -2x

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 2x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 2x + x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + x2 = 0 Solving -1 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x + x2 = 0 + 1 2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2x + x2 = 1 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 = 1 + 1 Reorder the terms: 1 + 2x + x2 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + 2x + x2 = 2 Factor a perfect square on the left side: (x + 1)(x + 1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + 1 = 1.414213562 Simplifying x + 1 = 1.414213562 Reorder the terms: 1 + x = 1.414213562 Solving 1 + x = 1.414213562 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 = 1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.414213562 + -1 x = 1.414213562 + -1 Combine like terms: 1.414213562 + -1 = 0.414213562 x = 0.414213562 Simplifying x = 0.414213562

Subproblem 2

x + 1 = -1.414213562 Simplifying x + 1 = -1.414213562 Reorder the terms: 1 + x = -1.414213562 Solving 1 + x = -1.414213562 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 = -1.414213562 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.414213562 + -1 x = -1.414213562 + -1 Combine like terms: -1.414213562 + -1 = -2.414213562 x = -2.414213562 Simplifying x = -2.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.414213562, -2.414213562}

Solution

x = {0.414213562, -2.414213562}

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