Question

Solve by using the square root property. Express the solution set in exact simplest form. (b-(1)/(5))^(2)=-(41)/(25) Express the solution set in exact simplest form.

Answer 1

To solve the equation (b - 1/5)^2 = -41/25 using the square root property, we need to isolate the square term on one side of the equation.

Step-by-step explanation:

To solve the equation (b - 1/5)^2 = -41/25 using the square root property, we need to isolate the square term on one side of the equation. First, expand the square on the left side: (b - 1/5) * (b - 1/5) = -41/25. Simplify the expression to get b^2 - 2/5b + 1/25 = -41/25. Move the constant term (1/25) to the right side: b^2 - 2/5b = -41/25 - 1/25 = -42/25. Finally, take the square root of both sides: b - 1/5 = ±√(-42/25). Solve for b by adding 1/5 to both sides: b = 1/5 ± √(-42/25).