Solve using the quadratic formula. 5z^2 − z − 7 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. z = _____ or z = _____

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Solve using the quadratic formula.  5z^2 − z − 7 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.  z = _____ or z = _____

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Identify coefficients: To solve the quadratic equation 5z^2 − z − 7 = 0 using the quadratic formula, we first identify the coefficients a, b, and c from the standard form of a quadratic equation ax^2 + bx + c = 0. Here, a = 5, b = -1, and c = -7.Apply quadratic formula: The quadratic formula is given by z = (-b ± √(b^2 - 4ac)) / (2a). We will substitute the values of a, b, and c into this formula to find the solutions for z.Calculate discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. For our equation, the discriminant is (-1)^2 - 4(5)(-7) = 1 + 140 = 141.Plug values into formula: Now, we can plug the values into the quadratic formula: z = (-(-1) ± √141) / (2 * 5). This simplifies to z = (1 ± √141) / 10.Calculate first solution: Since the discriminant is positive, we have two real and distinct solutions. We will calculate each solution separately, starting with the addition of the square root. z = (1 + √141) / 10 ≈ (1 + 11.874) / 10 ≈ 12.874 / 10 ≈ 1.29 when rounded to the nearest hundredth.Calculate second solution: Next, we calculate the solution with the subtraction of the square root. z = (1 - √141) / 10 ≈ (1 - 11.874) / 10 ≈ -10.874 / 10 ≈ -1.09 when rounded to the nearest hundredth.

Solve using the quadratic formula. $\newline$ $5z^2 - z - 7 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $z =$ _ or $z =$ _

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Solve using the quadratic formula.\newline5z2−z−7=05z^2 - z - 7 = 05z2−z−7=0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinez=z = z=_____ or z=z = z=_____

Solve using the quadratic formula. $\newline$ $5z^2 - z - 7 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $z =$ _ or $z =$ _