Solve the equation [tex]7x^2 + 8x + 1 = 0[/tex] using the quadratic formula.
Answer (2)
0\ then\ x_1=\frac{-b-\sqrt\Delta}{2a}\ and\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=8^2-4\cdot7\cdot1=64-28=36;\ \sqrt\Delta=\sqrt{36}=6\\\\x_1=\frac{-8-6}{2\cdot7}=\frac{-14}{14}=-1;\ x_2=\frac{-8+6}{2\cdot7}=\frac{-2}{14}=-\frac{1}{7}\\\\Answer:x=-1\ \vee\ x=-\frac{1}{7}"> 7 x 2 + 8 x + 1 = 0 a = 7 ; b = 8 ; c = 1 Δ = b 2 − 4 a c ; i f \DElta > 0 t h e n x 1 = 2 a − b − Δ an d x 2 = 2 a − b + Δ Δ = 8 2 − 4 ⋅ 7 ⋅ 1 = 64 − 28 = 36 ; Δ = 36 = 6 x 1 = 2 ⋅ 7 − 8 − 6 = 14 − 14 = − 1 ; x 2 = 2 ⋅ 7 − 8 + 6 = 14 − 2 = − 7 1 A n s w er : x = − 1 ∨ x = − 7 1
By applying the quadratic formula to the equation 7 x 2 + 8 x + 1 = 0 , we find two solutions: x = − 1 and x = − 7 1 . The calculation involves determining the coefficients, computing the discriminant, and then solving for x .
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