(x+2)x=3+4.10

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Solution for (x+2)x=3+4.10 equation:


Simplifying
(x + 2) * x = 3 + 4.10

Reorder the terms:
(2 + x) * x = 3 + 4.10

Reorder the terms for easier multiplication:
x(2 + x) = 3 + 4.10
(2 * x + x * x) = 3 + 4.10
(2x + x2) = 3 + 4.10

Combine like terms: 3 + 4.10 = 7.1
2x + x2 = 7.1

Solving
2x + x2 = 7.1

Solving for variable 'x'.

Reorder the terms:
-7.1 + 2x + x2 = 7.1 + -7.1

Combine like terms: 7.1 + -7.1 = 0.0
-7.1 + 2x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '7.1' to each side of the equation.
-7.1 + 2x + 7.1 + x2 = 0.0 + 7.1

Reorder the terms:
-7.1 + 7.1 + 2x + x2 = 0.0 + 7.1

Combine like terms: -7.1 + 7.1 = 0.0
0.0 + 2x + x2 = 0.0 + 7.1
2x + x2 = 0.0 + 7.1

Combine like terms: 0.0 + 7.1 = 7.1
2x + x2 = 7.1

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 = 7.1 + 1

Reorder the terms:
1 + 2x + x2 = 7.1 + 1

Combine like terms: 7.1 + 1 = 8.1
1 + 2x + x2 = 8.1

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8.1

Calculate the square root of the right side: 2.846049894

Break this problem into two subproblems by setting 
(x + 1) equal to 2.846049894 and -2.846049894.

Subproblem 1

x + 1 = 2.846049894 Simplifying x + 1 = 2.846049894 Reorder the terms: 1 + x = 2.846049894 Solving 1 + x = 2.846049894 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 = 2.846049894 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.846049894 + -1 x = 2.846049894 + -1 Combine like terms: 2.846049894 + -1 = 1.846049894 x = 1.846049894 Simplifying x = 1.846049894

Subproblem 2

x + 1 = -2.846049894 Simplifying x + 1 = -2.846049894 Reorder the terms: 1 + x = -2.846049894 Solving 1 + x = -2.846049894 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 = -2.846049894 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.846049894 + -1 x = -2.846049894 + -1 Combine like terms: -2.846049894 + -1 = -3.846049894 x = -3.846049894 Simplifying x = -3.846049894

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.846049894, -3.846049894}

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