(x+46)(55+x)=50

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Solution for (x+46)(55+x)=50 equation:


Simplifying
(x + 46)(55 + x) = 50

Reorder the terms:
(46 + x)(55 + x) = 50

Multiply (46 + x) * (55 + x)
(46(55 + x) + x(55 + x)) = 50
((55 * 46 + x * 46) + x(55 + x)) = 50
((2530 + 46x) + x(55 + x)) = 50
(2530 + 46x + (55 * x + x * x)) = 50
(2530 + 46x + (55x + x2)) = 50

Combine like terms: 46x + 55x = 101x
(2530 + 101x + x2) = 50

Solving
2530 + 101x + x2 = 50

Solving for variable 'x'.

Reorder the terms:
2530 + -50 + 101x + x2 = 50 + -50

Combine like terms: 2530 + -50 = 2480
2480 + 101x + x2 = 50 + -50

Combine like terms: 50 + -50 = 0
2480 + 101x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2480' to each side of the equation.
2480 + 101x + -2480 + x2 = 0 + -2480

Reorder the terms:
2480 + -2480 + 101x + x2 = 0 + -2480

Combine like terms: 2480 + -2480 = 0
0 + 101x + x2 = 0 + -2480
101x + x2 = 0 + -2480

Combine like terms: 0 + -2480 = -2480
101x + x2 = -2480

The x term is 101x.  Take half its coefficient (50.5).
Square it (2550.25) and add it to both sides.

Add '2550.25' to each side of the equation.
101x + 2550.25 + x2 = -2480 + 2550.25

Reorder the terms:
2550.25 + 101x + x2 = -2480 + 2550.25

Combine like terms: -2480 + 2550.25 = 70.25
2550.25 + 101x + x2 = 70.25

Factor a perfect square on the left side:
(x + 50.5)(x + 50.5) = 70.25

Calculate the square root of the right side: 8.381527307

Break this problem into two subproblems by setting 
(x + 50.5) equal to 8.381527307 and -8.381527307.

Subproblem 1

x + 50.5 = 8.381527307 Simplifying x + 50.5 = 8.381527307 Reorder the terms: 50.5 + x = 8.381527307 Solving 50.5 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = 8.381527307 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = 8.381527307 + -50.5 x = 8.381527307 + -50.5 Combine like terms: 8.381527307 + -50.5 = -42.118472693 x = -42.118472693 Simplifying x = -42.118472693

Subproblem 2

x + 50.5 = -8.381527307 Simplifying x + 50.5 = -8.381527307 Reorder the terms: 50.5 + x = -8.381527307 Solving 50.5 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50.5' to each side of the equation. 50.5 + -50.5 + x = -8.381527307 + -50.5 Combine like terms: 50.5 + -50.5 = 0.0 0.0 + x = -8.381527307 + -50.5 x = -8.381527307 + -50.5 Combine like terms: -8.381527307 + -50.5 = -58.881527307 x = -58.881527307 Simplifying x = -58.881527307

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-42.118472693, -58.881527307}

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