x(x-2)=74

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Solution for x(x-2)=74 equation:


Simplifying
x(x + -2) = 74

Reorder the terms:
x(-2 + x) = 74
(-2 * x + x * x) = 74
(-2x + x2) = 74

Solving
-2x + x2 = 74

Solving for variable 'x'.

Reorder the terms:
-74 + -2x + x2 = 74 + -74

Combine like terms: 74 + -74 = 0
-74 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + -2x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + -2x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + -2x + x2 = 0 + 74
-2x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
-2x + x2 = 74

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 = 74 + 1

Reorder the terms:
1 + -2x + x2 = 74 + 1

Combine like terms: 74 + 1 = 75
1 + -2x + x2 = 75

Factor a perfect square on the left side:
(x + -1)(x + -1) = 75

Calculate the square root of the right side: 8.660254038

Break this problem into two subproblems by setting 
(x + -1) equal to 8.660254038 and -8.660254038.

Subproblem 1

x + -1 = 8.660254038 Simplifying x + -1 = 8.660254038 Reorder the terms: -1 + x = 8.660254038 Solving -1 + x = 8.660254038 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 = 8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.660254038 + 1 x = 8.660254038 + 1 Combine like terms: 8.660254038 + 1 = 9.660254038 x = 9.660254038 Simplifying x = 9.660254038

Subproblem 2

x + -1 = -8.660254038 Simplifying x + -1 = -8.660254038 Reorder the terms: -1 + x = -8.660254038 Solving -1 + x = -8.660254038 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 = -8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.660254038 + 1 x = -8.660254038 + 1 Combine like terms: -8.660254038 + 1 = -7.660254038 x = -7.660254038 Simplifying x = -7.660254038

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.660254038, -7.660254038}

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