x(x+14)=64

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Solution for x(x+14)=64 equation:


Simplifying
x(x + 14) = 64

Reorder the terms:
x(14 + x) = 64
(14 * x + x * x) = 64
(14x + x2) = 64

Solving
14x + x2 = 64

Solving for variable 'x'.

Reorder the terms:
-64 + 14x + x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 14x + 64 + x2 = 0 + 64

Reorder the terms:
-64 + 64 + 14x + x2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 14x + x2 = 0 + 64
14x + x2 = 0 + 64

Combine like terms: 0 + 64 = 64
14x + x2 = 64

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 64 + 49

Reorder the terms:
49 + 14x + x2 = 64 + 49

Combine like terms: 64 + 49 = 113
49 + 14x + x2 = 113

Factor a perfect square on the left side:
(x + 7)(x + 7) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(x + 7) equal to 10.630145813 and -10.630145813.

Subproblem 1

x + 7 = 10.630145813 Simplifying x + 7 = 10.630145813 Reorder the terms: 7 + x = 10.630145813 Solving 7 + x = 10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 10.630145813 + -7 Combine like terms: 7 + -7 = 0 0 + x = 10.630145813 + -7 x = 10.630145813 + -7 Combine like terms: 10.630145813 + -7 = 3.630145813 x = 3.630145813 Simplifying x = 3.630145813

Subproblem 2

x + 7 = -10.630145813 Simplifying x + 7 = -10.630145813 Reorder the terms: 7 + x = -10.630145813 Solving 7 + x = -10.630145813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -10.630145813 + -7 Combine like terms: 7 + -7 = 0 0 + x = -10.630145813 + -7 x = -10.630145813 + -7 Combine like terms: -10.630145813 + -7 = -17.630145813 x = -17.630145813 Simplifying x = -17.630145813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.630145813, -17.630145813}

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