1764=x(x+37)

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Solution for 1764=x(x+37) equation:


Simplifying
1764 = x(x + 37)

Reorder the terms:
1764 = x(37 + x)
1764 = (37 * x + x * x)
1764 = (37x + x2)

Solving
1764 = 37x + x2

Solving for variable 'x'.

Reorder the terms:
1764 + -37x + -1x2 = 37x + -37x + x2 + -1x2

Combine like terms: 37x + -37x = 0
1764 + -37x + -1x2 = 0 + x2 + -1x2
1764 + -37x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1764 + -37x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1764 + 37x + x2 = 0

Move the constant term to the right:

Add '1764' to each side of the equation.
-1764 + 37x + 1764 + x2 = 0 + 1764

Reorder the terms:
-1764 + 1764 + 37x + x2 = 0 + 1764

Combine like terms: -1764 + 1764 = 0
0 + 37x + x2 = 0 + 1764
37x + x2 = 0 + 1764

Combine like terms: 0 + 1764 = 1764
37x + x2 = 1764

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = 1764 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 1764 + 342.25

Combine like terms: 1764 + 342.25 = 2106.25
342.25 + 37x + x2 = 2106.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 2106.25

Calculate the square root of the right side: 45.893899377

Break this problem into two subproblems by setting 
(x + 18.5) equal to 45.893899377 and -45.893899377.

Subproblem 1

x + 18.5 = 45.893899377 Simplifying x + 18.5 = 45.893899377 Reorder the terms: 18.5 + x = 45.893899377 Solving 18.5 + x = 45.893899377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 45.893899377 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 45.893899377 + -18.5 x = 45.893899377 + -18.5 Combine like terms: 45.893899377 + -18.5 = 27.393899377 x = 27.393899377 Simplifying x = 27.393899377

Subproblem 2

x + 18.5 = -45.893899377 Simplifying x + 18.5 = -45.893899377 Reorder the terms: 18.5 + x = -45.893899377 Solving 18.5 + x = -45.893899377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -45.893899377 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -45.893899377 + -18.5 x = -45.893899377 + -18.5 Combine like terms: -45.893899377 + -18.5 = -64.393899377 x = -64.393899377 Simplifying x = -64.393899377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.393899377, -64.393899377}

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