Factor the quadratic equation:

\[ 7x^2 - 31x + 20 = 0 \]

Provide the steps to solve this equation.

7 x 2 − 31 x + 20 = 0 First, remove the coefficient by division So 7 7 x 2 ​ − 7 31 x ​ + 7 20 ​ = 0 Then, cancel out 7 20 ​ So, x 2 − 7 31 x ​ + 7 20 ​ − 7 20 ​ = − 7 20 ​ Then take half of the coefficient, then square it. 2 − 7 31 ​ ​ = 14 37 ​ ( − 14 37 ​ ) 2 = 196 961 ​ So, The equation already looks like this: x 2 − 7 31 ​ + 196 961 ​ = − 7 20 ​ + 196 961 ​ So, x 2 − 7 31 ​ + 196 961 ​ = 196 401 ​ Then factor the left side of the equation: ( x − 14 31 ​ ) 2 = 196 401 ​ Then square both sides: x − 14 31 ​ = 196 401 ​ ​

Answered by Edmund | 2024-06-10

7 x 2 − 31 x + 20 = 0 Δ = ( − 31 ) 2 − 4.7.20 = 961 − 560 = 401 x = 2 ∗ 7 31 \pmsqrt 401 ​ = 14 31 ± 401 ​ ​

Answered by Ryan2 | 2024-06-10

To factor the quadratic equation 7 x 2 − 31 x + 20 = 0 , we first find two numbers that replace the middle term, ultimately leading us to factor it as ( 7 x − 5 ) ( x − 4 ) = 0 . The solutions to the equation are x = 7 5 ​ and x = 4 .
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Answered by Edmund | 2024-12-23