Solve using the quadratic formula.8n2−6n−8=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.n=_____ or n=_____
Q. Solve using the quadratic formula.8n2−6n−8=0Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.n=_____ or n=_____
Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation8n2−6n−8=0.a=8, b=−6, c=−8
Write quadratic formula: Write down the quadratic formula: n=2a−b±b2−4ac.
Substitute values: Substitute the values of a, b, and c into the quadratic formula.n=2⋅8−(−6)±(−6)2−4⋅8⋅(−8)
Calculate discriminant: Simplify the equation by calculating the discriminant b2−4ac.Discriminant = (−6)2−4⋅8⋅(−8) = 36+256 = 292
Insert discriminant: Insert the value of the discriminant back into the quadratic formula. n=166±292
Simplify square root: Simplify the square root of the discriminant if possible. 292 cannot be simplified further as a square root of an integer.
Calculate solutions: Calculate the two possible solutions for n.n=166+292 or n=166−292
Round values: Round the values of n to the nearest hundredth, if required.n≈(6+17.09)/16 or n≈(6−17.09)/16n≈23.09/16 or n≈−11.09/16n≈1.44 or n≈−0.69
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