0.45(x+50)0.18(x+40)=-27

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Solution for 0.45(x+50)0.18(x+40)=-27 equation: 


Simplifying
0.45(x + 50) * 0.18(x + 40) = -27

Reorder the terms:
0.45(50 + x) * 0.18(x + 40) = -27

Reorder the terms:
0.45(50 + x) * 0.18(40 + x) = -27

Reorder the terms for easier multiplication:
0.45 * 0.18(50 + x)(40 + x) = -27

Multiply 0.45 * 0.18
0.081(50 + x)(40 + x) = -27

Multiply (50 + x) * (40 + x)
0.081(50(40 + x) + x(40 + x)) = -27
0.081((40 * 50 + x * 50) + x(40 + x)) = -27
0.081((2000 + 50x) + x(40 + x)) = -27
0.081(2000 + 50x + (40 * x + x * x)) = -27
0.081(2000 + 50x + (40x + x2)) = -27

Combine like terms: 50x + 40x = 90x
0.081(2000 + 90x + x2) = -27
(2000 * 0.081 + 90x * 0.081 + x2 * 0.081) = -27
(162 + 7.29x + 0.081x2) = -27

Solving
162 + 7.29x + 0.081x2 = -27

Solving for variable 'x'.

Reorder the terms:
162 + 27 + 7.29x + 0.081x2 = -27 + 27

Combine like terms: 162 + 27 = 189
189 + 7.29x + 0.081x2 = -27 + 27

Combine like terms: -27 + 27 = 0
189 + 7.29x + 0.081x2 = 0

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

Divide each side by '0.081'.
2333.333333 + 90x + x2 = 0

Move the constant term to the right:

Add '-2333.333333' to each side of the equation.
2333.333333 + 90x + -2333.333333 + x2 = 0 + -2333.333333

Reorder the terms:
2333.333333 + -2333.333333 + 90x + x2 = 0 + -2333.333333

Combine like terms: 2333.333333 + -2333.333333 = 0.000000
0.000000 + 90x + x2 = 0 + -2333.333333
90x + x2 = 0 + -2333.333333

Combine like terms: 0 + -2333.333333 = -2333.333333
90x + x2 = -2333.333333

The x term is 90x.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90x + 2025 + x2 = -2333.333333 + 2025

Reorder the terms:
2025 + 90x + x2 = -2333.333333 + 2025

Combine like terms: -2333.333333 + 2025 = -308.333333
2025 + 90x + x2 = -308.333333

Factor a perfect square on the left side:
(x + 45)(x + 45) = -308.333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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