x(x+8)=10

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Solution for x(x+8)=10 equation:


Simplifying
x(x + 8) = 10

Reorder the terms:
x(8 + x) = 10
(8 * x + x * x) = 10
(8x + x2) = 10

Solving
8x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 8x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 8x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 8x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 8x + x2 = 0 + 10
8x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
8x + x2 = 10

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 10 + 16

Reorder the terms:
16 + 8x + x2 = 10 + 16

Combine like terms: 10 + 16 = 26
16 + 8x + x2 = 26

Factor a perfect square on the left side:
(x + 4)(x + 4) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + 4) equal to 5.099019514 and -5.099019514.

Subproblem 1

x + 4 = 5.099019514 Simplifying x + 4 = 5.099019514 Reorder the terms: 4 + x = 5.099019514 Solving 4 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.099019514 + -4 x = 5.099019514 + -4 Combine like terms: 5.099019514 + -4 = 1.099019514 x = 1.099019514 Simplifying x = 1.099019514

Subproblem 2

x + 4 = -5.099019514 Simplifying x + 4 = -5.099019514 Reorder the terms: 4 + x = -5.099019514 Solving 4 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.099019514 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.099019514 + -4 x = -5.099019514 + -4 Combine like terms: -5.099019514 + -4 = -9.099019514 x = -9.099019514 Simplifying x = -9.099019514

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.099019514, -9.099019514}

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