x(x+4)-10=18

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Solution for x(x+4)-10=18 equation:


Simplifying
x(x + 4) + -10 = 18

Reorder the terms:
x(4 + x) + -10 = 18
(4 * x + x * x) + -10 = 18
(4x + x2) + -10 = 18

Reorder the terms:
-10 + 4x + x2 = 18

Solving
-10 + 4x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
-10 + -18 + 4x + x2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + 4x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 4x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 4x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 4x + x2 = 0 + 28
4x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
4x + x2 = 28

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 = 28 + 4

Reorder the terms:
4 + 4x + x2 = 28 + 4

Combine like terms: 28 + 4 = 32
4 + 4x + x2 = 32

Factor a perfect square on the left side:
(x + 2)(x + 2) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + 2) equal to 5.656854249 and -5.656854249.

Subproblem 1

x + 2 = 5.656854249 Simplifying x + 2 = 5.656854249 Reorder the terms: 2 + x = 5.656854249 Solving 2 + x = 5.656854249 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 = 5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.656854249 + -2 x = 5.656854249 + -2 Combine like terms: 5.656854249 + -2 = 3.656854249 x = 3.656854249 Simplifying x = 3.656854249

Subproblem 2

x + 2 = -5.656854249 Simplifying x + 2 = -5.656854249 Reorder the terms: 2 + x = -5.656854249 Solving 2 + x = -5.656854249 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 = -5.656854249 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.656854249 + -2 x = -5.656854249 + -2 Combine like terms: -5.656854249 + -2 = -7.656854249 x = -7.656854249 Simplifying x = -7.656854249

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.656854249, -7.656854249}

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