Solve using the quadratic formula.9v2+7v+1=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.v= _____ or v= _____
Q. Solve using the quadratic formula.9v2+7v+1=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.v= _____ or v= _____
Identify coefficients: Identify the coefficients of the quadratic equation.The quadratic equation is in the form av2+bv+c=0. For the equation 9v2+7v+1=0, the coefficients are:a = 9b = 7c = 1
Write formula: Write down the quadratic formula.The quadratic formula is given by v=2a−b±b2−4ac.
Substitute values: Substitute the values of a, b, and c into the quadratic formula.Substitute a=9, b=7, and c=1 into the quadratic formula to find the values of v.v=2⋅9−7±72−4⋅9⋅1
Calculate discriminant: Calculate the discriminant (the part under the square root). The discriminant is b2−4ac. Discriminant = 72−4×9×1 Discriminant = 49−36 Discriminant = 13
Calculate solutions: Calculate the two possible solutions for v using the discriminant.v=18−7±13
Simplify and round: Simplify the solutions and round to the nearest hundredth if necessary.First solution:v=18−7+13v≈18−7+3.61v≈18−3.39v≈−0.19Second solution:v=18−7−13v≈18−7−3.61v≈18−10.61v≈−0.59
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