x(x+76)=768

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Solution for x(x+76)=768 equation:


Simplifying
x(x + 76) = 768

Reorder the terms:
x(76 + x) = 768
(76 * x + x * x) = 768
(76x + x2) = 768

Solving
76x + x2 = 768

Solving for variable 'x'.

Reorder the terms:
-768 + 76x + x2 = 768 + -768

Combine like terms: 768 + -768 = 0
-768 + 76x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '768' to each side of the equation.
-768 + 76x + 768 + x2 = 0 + 768

Reorder the terms:
-768 + 768 + 76x + x2 = 0 + 768

Combine like terms: -768 + 768 = 0
0 + 76x + x2 = 0 + 768
76x + x2 = 0 + 768

Combine like terms: 0 + 768 = 768
76x + x2 = 768

The x term is 76x.  Take half its coefficient (38).
Square it (1444) and add it to both sides.

Add '1444' to each side of the equation.
76x + 1444 + x2 = 768 + 1444

Reorder the terms:
1444 + 76x + x2 = 768 + 1444

Combine like terms: 768 + 1444 = 2212
1444 + 76x + x2 = 2212

Factor a perfect square on the left side:
(x + 38)(x + 38) = 2212

Calculate the square root of the right side: 47.031904065

Break this problem into two subproblems by setting 
(x + 38) equal to 47.031904065 and -47.031904065.

Subproblem 1

x + 38 = 47.031904065 Simplifying x + 38 = 47.031904065 Reorder the terms: 38 + x = 47.031904065 Solving 38 + x = 47.031904065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 47.031904065 + -38 Combine like terms: 38 + -38 = 0 0 + x = 47.031904065 + -38 x = 47.031904065 + -38 Combine like terms: 47.031904065 + -38 = 9.031904065 x = 9.031904065 Simplifying x = 9.031904065

Subproblem 2

x + 38 = -47.031904065 Simplifying x + 38 = -47.031904065 Reorder the terms: 38 + x = -47.031904065 Solving 38 + x = -47.031904065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = -47.031904065 + -38 Combine like terms: 38 + -38 = 0 0 + x = -47.031904065 + -38 x = -47.031904065 + -38 Combine like terms: -47.031904065 + -38 = -85.031904065 x = -85.031904065 Simplifying x = -85.031904065

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.031904065, -85.031904065}

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