Final answer:
To find the value of x that satisfies the equation (4x – 1)^2 = 20x – 5, we expand and simplify the equation, combine like terms, and solve for x using the quadratic formula. The solutions are x = 1/2 and x = 3/8.
Step-by-step explanation:
The given equation is (4x – 1)^2 = 20x – 5. To find the value of x that satisfies this equation, we will expand and simplify the left side of the equation.
(4x – 1)^2 = (4x – 1)(4x – 1) = 16x^2 – 8x + 1. Now we have the equation 16x^2 – 8x + 1 = 20x – 5.
Combining like terms, we get 16x^2 – 28x + 6 = 0. This is a quadratic equation, and we can solve it using the quadratic formula.
The quadratic formula is x = (-b ± sqrt(b^2 – 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 16, b = -28, and c = 6.
Plugging these values into the formula, we get x = (-(-28) ± sqrt((-28)^2 – 4(16)(6))) / (2(16)). After simplifying, we find two solutions: x = 1/2 and x = 3/8.