Find one value of x that is a solution to the equation: {:[(4x-1)^(2)=20 x-5],[x=]:}

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Find one value of  x that is a solution to the equation:  {:[(4x-1)^(2)=20 x-5],[x=]:}

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Expand squared term: Expand the squared term on the left side of the equation. (4x - 1)² = (4x - 1)(4x - 1) = 16x² - 4x - 4x + 1 Combine like terms. 16x² - 8x + 1 = 20x - 5Combine like terms: Move all terms to one side to set the equation to zero. 16x² - 8x + 1 - 20x + 5 = 0 Combine like terms. 16x² - 28x + 6 = 0Move terms to one side: Factor the quadratic equation, if possible. This step involves finding two numbers that multiply to 16 * 6 = 96 and add up to -28. However, since 96 is not easily factored into two numbers that add up to -28, we might need to use the quadratic formula to find the roots.Factor quadratic equation: Use the quadratic formula to find the values of x. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a = 16, b = -28, and c = 6. Calculate the discriminant: b² - 4ac = (-28)² - 4(16)(6) = 784 - 384 = 400Use quadratic formula: Calculate the square root of the discriminant. √400 = 20Calculate discriminant: Plug the values into the quadratic formula. x = (-(-28) ± 20) / (2 * 16) x = (28 ± 20) / 32Calculate square root: Solve for the two possible values of x. x = (28 + 20) / 32 or x = (28 - 20) / 32 x = 48 / 32 or x = 8 / 32 Simplify the fractions. x = 3/2 or x = 1/4Plug values into formula: Choose one value of x as the solution. We can choose either x = 3/2 or x = 1/4 as the solution to the equation. Let's choose x = 3/2 for this prompt.

Find one value of $x$ that is a solution to the equation: $\newline$ $(4 x-1)^{2}=20 x-5$ $\newline$ $x=$

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Find one value of x x x that is a solution to the equation:\newline(4x−1)2=20x−5 (4 x-1)^{2}=20 x-5 (4x−1)2=20x−5\newlinex= x= x=

Find one value of $x$ that is a solution to the equation: $\newline$ $(4 x-1)^{2}=20 x-5$ $\newline$ $x=$