Solve using the quadratic formula.9x2+7x−7=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.x=_____ or x=_____
Q. Solve using the quadratic formula.9x2+7x−7=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.x=_____ or x=_____
Recall quadratic formula: Recall the quadratic formula, which is x=2a−b±b2−4ac. We will use this formula to find the values of x.
Substitute coefficients: Substitute the coefficients a, b, and c into the quadratic formula. This gives us x=2(9)−(7)±(7)2−4(9)(−7).
Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4ac. This is (7)2−4(9)(−7)=49+252=301.
Insert discriminant: Insert the discriminant back into the quadratic formula: x=18−7±301.
Simplify square root: Simplify the square root of the discriminant if possible. Since 301 is not a perfect square, we leave it as 301.
Calculate positive solution: Calculate the two possible values for x using the plus and minus in the quadratic formula. First, the positive solution: x=18−7+301.
Calculate negative solution: Calculate the negative solution: x=18−7−301.
Express solutions as decimals: Since the square root of 301 cannot be simplified further, we can express the solutions as decimals if required. The decimal approximations are x≈(−7+301)/18≈0.79 and x≈(−7−301)/18≈−1.46, rounded to the nearest hundredth.
More problems from Solve a quadratic equation using the quadratic formula