Solve using the quadratic formula. 9q^2 − 2q − 5 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. q = _____ or q = _____

Question

Solve using the quadratic formula.  9q^2 − 2q − 5 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.  q = _____ or q = _____

Bytelearn · Accepted Answer

Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation 9q^2 − 2q − 5 = 0. a = 9, b = -2, c = -5Write quadratic formula: Write down the quadratic formula: q = (-b ± sqrt(b^2 - 4ac)) / (2a).Substitute values: Substitute the values of a, b, and c into the quadratic formula. q = (-(-2) ± sqrt((-2)^2 - 4*9*(-5))) / (2*9)Calculate discriminant: Simplify the equation by calculating the discriminant (the part under the square root). Discriminant = (-2)^2 - 4*9*(-5) = 4 + 180 = 184Insert discriminant: Insert the discriminant back into the quadratic formula. q = (2 ± sqrt(184)) / 18Simplify square root: Simplify the square root of the discriminant. sqrt(184) is not a perfect square, so we will leave it as sqrt(184) for now.Calculate solutions: Calculate the two possible solutions for q. q = (2 + sqrt(184)) / 18 or q = (2 - sqrt(184)) / 18Round values: If necessary, round the values of q to the nearest hundredth. q ≈ (2 + 13.56) / 18 or q ≈ (2 - 13.56) / 18 q ≈ 15.56 / 18 or q ≈ -11.56 / 18 q ≈ 0.86 or q ≈ -0.64

Solve using the quadratic formula. $\newline$ $9q^2 - 2q - 5 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $q =$ _ or $q =$ _

Full solution

More problems from Solve a quadratic equation using the quadratic formula

Related topics

Solve using the quadratic formula.\newline9q2−2q−5=09q^2 - 2q - 5 = 09q2−2q−5=0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = q=_____ or q=q = q=_____

Solve using the quadratic formula. $\newline$ $9q^2 - 2q - 5 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $q =$ _ or $q =$ _