Question

solve 6x² + 19x - 7 = 0 by using the quadratic formula. note that a ± b means a - b or a + b. x = (-19 - 23)/12, x = (-19 + 23)/12, x = -42/12 or x = 4/12, x = -7/2, x = 1/3 simplify step 4: check start with x = -7/2. 6x² + 19x - 7 = 0 6( )² + 19( ) - 7 =? 0 6·49/4 - 19·7/2 - 7 =? 0 147/2 - 133/2 - 7 =? 0 14/2 - 7 =? 0 0 = 0 true

Explanation:

Step1: Identify coefficients

\(a=6\), \(b=19\), \(c=-7\)

Step2: Calculate discriminant

\(D=19^2 - 4(6)(-7)=361+168=529\)

Step3: Apply quadratic formula

\(x=\frac{-19\pm\sqrt{529}}{2(6)}=\frac{-19\pm23}{12}\)

Step4: Solve for x

\(x=\frac{-19+23}{12}=\frac{4}{12}=\frac{1}{3}\); \(x=\frac{-19-23}{12}=\frac{-42}{12}=-\frac{7}{2}\)

Answer:

\(x = \frac{1}{3}\), \(x = -\frac{7}{2}\)