(x+40)(x+60)=600

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Solution for (x+40)(x+60)=600 equation:


Simplifying
(x + 40)(x + 60) = 600

Reorder the terms:
(40 + x)(x + 60) = 600

Reorder the terms:
(40 + x)(60 + x) = 600

Multiply (40 + x) * (60 + x)
(40(60 + x) + x(60 + x)) = 600
((60 * 40 + x * 40) + x(60 + x)) = 600
((2400 + 40x) + x(60 + x)) = 600
(2400 + 40x + (60 * x + x * x)) = 600
(2400 + 40x + (60x + x2)) = 600

Combine like terms: 40x + 60x = 100x
(2400 + 100x + x2) = 600

Solving
2400 + 100x + x2 = 600

Solving for variable 'x'.

Reorder the terms:
2400 + -600 + 100x + x2 = 600 + -600

Combine like terms: 2400 + -600 = 1800
1800 + 100x + x2 = 600 + -600

Combine like terms: 600 + -600 = 0
1800 + 100x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1800' to each side of the equation.
1800 + 100x + -1800 + x2 = 0 + -1800

Reorder the terms:
1800 + -1800 + 100x + x2 = 0 + -1800

Combine like terms: 1800 + -1800 = 0
0 + 100x + x2 = 0 + -1800
100x + x2 = 0 + -1800

Combine like terms: 0 + -1800 = -1800
100x + x2 = -1800

The x term is 100x.  Take half its coefficient (50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
100x + 2500 + x2 = -1800 + 2500

Reorder the terms:
2500 + 100x + x2 = -1800 + 2500

Combine like terms: -1800 + 2500 = 700
2500 + 100x + x2 = 700

Factor a perfect square on the left side:
(x + 50)(x + 50) = 700

Calculate the square root of the right side: 26.457513111

Break this problem into two subproblems by setting 
(x + 50) equal to 26.457513111 and -26.457513111.

Subproblem 1

x + 50 = 26.457513111 Simplifying x + 50 = 26.457513111 Reorder the terms: 50 + x = 26.457513111 Solving 50 + x = 26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 26.457513111 + -50 Combine like terms: 50 + -50 = 0 0 + x = 26.457513111 + -50 x = 26.457513111 + -50 Combine like terms: 26.457513111 + -50 = -23.542486889 x = -23.542486889 Simplifying x = -23.542486889

Subproblem 2

x + 50 = -26.457513111 Simplifying x + 50 = -26.457513111 Reorder the terms: 50 + x = -26.457513111 Solving 50 + x = -26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -26.457513111 + -50 Combine like terms: 50 + -50 = 0 0 + x = -26.457513111 + -50 x = -26.457513111 + -50 Combine like terms: -26.457513111 + -50 = -76.457513111 x = -76.457513111 Simplifying x = -76.457513111

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-23.542486889, -76.457513111}

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