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

Question

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

Bytelearn · Accepted Answer

Write Quadratic Formula: Write down the quadratic formula. The quadratic formula is used to solve equations of the form ax^2 + bx + c = 0. The formula is: r = (-b ± √(b^2 - 4ac)) / (2a)Identify Coefficients: Identify the coefficients a, b, and c from the equation 9r^2 + 2r − 2 = 0. Here, a = 9, b = 2, and c = -2.Substitute Values: Substitute the values of a, b, and c into the quadratic formula. r = (-(2) ± √((2)^2 - 4(9)(-2))) / (2(9))Simplify Discriminant: Simplify the expression under the square root (the discriminant). √((2)^2 - 4(9)(-2)) = √(4 + 72) = √76Simplify Formula: Simplify the quadratic formula with the values. r = (-2 ± √76) / 18Simplify Square Root: Simplify the square root √76 to its simplest radical form. √76 can be written as √(4*19), which simplifies to 2√19.Substitute Square Root: Substitute the simplified square root back into the formula. r = (-2 ± 2√19) / 18Factor Out Common Factor: Simplify the expression by factoring out the common factor of 2 in the numerator. r = 2(-1 ± √19) / 18 r = (-1 ± √19) / 9Write Two Solutions: Write down the two solutions for r. r = (-1 + √19) / 9 or r = (-1 - √19) / 9

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

Full solution

More problems from Solve a quadratic equation using the quadratic formula

Related topics

Solve using the quadratic formula.\newline9r2+2r−2=09r^2 + 2r - 2 = 09r2+2r−2=0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = r=_____ or r=r = r=_____

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