Question

-b+ sqrt(60-6b)=-10
Solve step by step

Answer 1

Simple steps

Answer 2

1. Subtract sqrt(60-6b) from both sides of the equation:

-b = -10 - sqrt(60-6b)

2. Square both sides of the equation to eliminate the square root:

b^2 = 100 + 20sqrt(60-6b) + 60-6b

3. Rearrange the equation to isolate the square root term:

b^2 + 6b - 160 = 20sqrt(60-6b)

4. Square both sides of the equation again to eliminate the square root:

(b^2 + 6b - 160)^2 = 400(60-6b)

b^4 + 12b^3 - 320b^2 + 12b^3 + 144b^2 - 3840b + 1600 = 2400 - 240b

5. Simplify and rearrange the equation:

b^4 + 24b^3 - 476b^2 + 3600b - 800 = 0

6. This fourth-degree polynomial equation does not have a simple solution, and it may require numerical methods or advanced algebraic techniques to solve.

Answer 3

Apologies for the confusion earlier. Here are the simplified steps to solve the equation:

Given equation: -b + sqrt(60-6b) = -10

1. Square both sides:
(-b + sqrt(60-6b))^2 = (-10)^2
b^2 - 2b*sqrt(60-6b) + (60-6b) = 100

2. Rearrange the equation:
b^2 - 2b*sqrt(60-6b) + 60 - 6b - 100 = 0
b^2 - 2b*sqrt(60-6b) - 6b - 40 = 0

3. Let's say sqrt(60-6b) = x:
b^2 - 2bx - 6b - 40 = 0

4. Substitute x back into the equation:
b^2 - 2b(sqrt(60-6b)) - 6b - 40 = 0

5. Now, you can solve for b by isolating the terms with b on one side. This may require further manipulation and simplification.