Solve for g.8g2−18g−5=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.g= ____
Q. Solve for g.8g2−18g−5=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.g= ____
Given quadratic equation: We are given the quadratic equation8g2−18g−5=0. To solve for g, we can use the quadratic formulag=2a−b±b2−4ac, where a=8, b=−18, and c=−5.
Calculate discriminant: First, calculate the discriminant Δ=b2−4ac. Here, Δ=(−18)2−4×8×(−5).
Find square root of discriminant: Perform the calculation: Δ=324+160=484.
Apply quadratic formula: Now, find the square root of the discriminant: Δ=484=22.
Simplify expression: Apply the quadratic formula: g=2×8−(−18)±22.
Find two possible values for g: Simplify the expression: g=1618±22.
Calculate first value: Find the two possible values for g: g=1618+22 and g=1618−22.
Simplify fraction: Calculate the first value: g=1640.
Calculate second value: Simplify the fraction: g=25.
Simplify fraction: Calculate the second value: g=16−4.
Simplify fraction: Calculate the second value: g=−164.Simplify the fraction: g=−41.