Solve using the quadratic formula. 8r^2 + 5r − 7 = 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.  8r^2 + 5r − 7 = 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

Identify Coefficients: To solve the quadratic equation 8r^2 + 5r − 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 = 8, b = 5, and c = -7.Apply Quadratic Formula: The quadratic formula is given by r = (-b ± √(b^2 - 4ac)) / (2a). We will substitute the values of a, b, and c into this formula to find the solutions for r.Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. This is 5^2 - 4(8)(-7) = 25 + 224 = 249.Plug Values into Formula: Now, we can plug the values into the quadratic formula: r = (-5 ± √249) / (16). Since 249 is not a perfect square, we will leave the square root as is for now.Find Solutions: We have two possible solutions for r, corresponding to the '±' in the formula. The first solution is r = (-5 + √249) / (16), and the second solution is r = (-5 - √249) / (16).Simplify Solutions: To simplify the solutions, we can leave them in the form of fractions or approximate them as decimals. The square root of 249 cannot be simplified further, so we will leave it as √249. The fraction cannot be simplified further either, so the solutions in fraction form are r = (-5 + √249) / (16) and r = (-5 - √249) / (16).Approximate Decimal Solutions: If we want to express the solutions as decimals, we can use a calculator to approximate √249 and then divide by 16. The approximate values are r ≈ (-5 + 15.78) / 16 ≈ 0.67 and r ≈ (-5 - 15.78) / 16 ≈ -1.30, rounded to the nearest hundredth.

Solve using the quadratic formula. $\newline$ $8r^2 + 5r - 7 = 0$ $\newline$ 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.\newline8r2+5r−7=08r^2 + 5r - 7 = 08r2+5r−7=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. $\newline$ $8r^2 + 5r - 7 = 0$ $\newline$ Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. $\newline$ $r =$ _ or $r =$ _