(x+60)(x+50)=1000

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Solution for (x+60)(x+50)=1000 equation:


Simplifying
(x + 60)(x + 50) = 1000

Reorder the terms:
(60 + x)(x + 50) = 1000

Reorder the terms:
(60 + x)(50 + x) = 1000

Multiply (60 + x) * (50 + x)
(60(50 + x) + x(50 + x)) = 1000
((50 * 60 + x * 60) + x(50 + x)) = 1000
((3000 + 60x) + x(50 + x)) = 1000
(3000 + 60x + (50 * x + x * x)) = 1000
(3000 + 60x + (50x + x2)) = 1000

Combine like terms: 60x + 50x = 110x
(3000 + 110x + x2) = 1000

Solving
3000 + 110x + x2 = 1000

Solving for variable 'x'.

Reorder the terms:
3000 + -1000 + 110x + x2 = 1000 + -1000

Combine like terms: 3000 + -1000 = 2000
2000 + 110x + x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
2000 + 110x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + 110x + -2000 + x2 = 0 + -2000

Reorder the terms:
2000 + -2000 + 110x + x2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + 110x + x2 = 0 + -2000
110x + x2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
110x + x2 = -2000

The x term is 110x.  Take half its coefficient (55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
110x + 3025 + x2 = -2000 + 3025

Reorder the terms:
3025 + 110x + x2 = -2000 + 3025

Combine like terms: -2000 + 3025 = 1025
3025 + 110x + x2 = 1025

Factor a perfect square on the left side:
(x + 55)(x + 55) = 1025

Calculate the square root of the right side: 32.015621187

Break this problem into two subproblems by setting 
(x + 55) equal to 32.015621187 and -32.015621187.

Subproblem 1

x + 55 = 32.015621187 Simplifying x + 55 = 32.015621187 Reorder the terms: 55 + x = 32.015621187 Solving 55 + x = 32.015621187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = 32.015621187 + -55 Combine like terms: 55 + -55 = 0 0 + x = 32.015621187 + -55 x = 32.015621187 + -55 Combine like terms: 32.015621187 + -55 = -22.984378813 x = -22.984378813 Simplifying x = -22.984378813

Subproblem 2

x + 55 = -32.015621187 Simplifying x + 55 = -32.015621187 Reorder the terms: 55 + x = -32.015621187 Solving 55 + x = -32.015621187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = -32.015621187 + -55 Combine like terms: 55 + -55 = 0 0 + x = -32.015621187 + -55 x = -32.015621187 + -55 Combine like terms: -32.015621187 + -55 = -87.015621187 x = -87.015621187 Simplifying x = -87.015621187

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-22.984378813, -87.015621187}

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