Solve using the quadratic formula. j^2 − 5j + 1 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. j = _____ or j = _____

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Solve using the quadratic formula.  j^2 − 5j + 1 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.  j = _____ or j = _____

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Quadratic Formula Definition: The quadratic formula is given by j = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation in the form aj^2 + bj + c = 0. For our equation, a = 1, b = -5, and c = 1.Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. For our equation, this is (-5)^2 - 4(1)(1) = 25 - 4 = 21.Apply Quadratic Formula: Now, apply the quadratic formula with the values of a, b, and c. We have j = (-(-5) ± √21) / (2 * 1) = (5 ± √21) / 2.Simplify Solutions: Since √21 cannot be simplified into a perfect square, we will leave it as is under the square root. The two solutions for j are j = (5 + √21) / 2 and j = (5 - √21) / 2.Calculate Decimal Approximations: To express the solutions as decimals rounded to the nearest hundredth, we calculate each one. For j = (5 + √21) / 2, the approximate value is (5 + 4.58) / 2 ≈ 9.58 / 2 ≈ 4.79. For j = (5 - √21) / 2, the approximate value is (5 - 4.58) / 2 ≈ 0.42 / 2 ≈ 0.21.

Solve using the quadratic formula. $\newline$ $j^2 - 5j + 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $j =$ _ or $j =$ _

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Solve using the quadratic formula.\newlinej2−5j+1=0j^2 - 5j + 1 = 0j2−5j+1=0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = j= _____ or j=j = j= _____

Solve using the quadratic formula. $\newline$ $j^2 - 5j + 1 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $j =$ _ or $j =$ _