How do I solve a quadratic equation like this:

\[ x^2 - 9x = -14 \]

Bring everything over to one side. x² -9x=-14 x²-9x+14=0 Now it is an easy trinomial so you need to find two numbers that add up to -9 and multiply to equal 14. The two numbers are -7 and -2. x²-9x+14=0 (x-7)(x-2)=0 x= 7 and 2

Answered by madison12340 | 2024-06-10

x 2 − 9 x = − 14 x 2 − 9 x + 14 = 0 − − − − − − − − − − − − − − − − − − − − − 9 = − 7 + ( − 2 ) 14 = − 7 ⋅ ( − 2 ) − − − − − − − − − − − − − − − − − − − − x 2 − 9 x + 14 = ( x − 7 ) ( x − 2 ) ( x − 7 ) ( x − 2 ) = 0 ⟺ x − 7 = 0 or x − 2 = 0 x = 7 or x = 2
x 2 − 9 x + 14 = 0 a = 1 ; b = − 9 ; c = 14 Δ = b 2 − 4 a c Δ = ( − 9 ) 2 − 4 ⋅ 1 ⋅ 14 = 81 − 56 = 25 x 1 ​ = 2 a − b − Δ ​ ​ → x 1 ​ = 2 ⋅ 1 9 − 25 ​ ​ = 2 9 − 5 ​ = 2 4 ​ = 2 x 2 ​ = 2 a − b + Δ ​ ​ → x 2 ​ = 2 ⋅ 1 9 + 25 ​ ​ = 2 9 + 5 ​ = 2 14 ​ = 7

Answered by Anonymous | 2024-06-10

To solve the equation x 2 − 9 x = − 14 , we rearranged it to form x 2 − 9 x + 14 = 0 and factored it, yielding solutions of x = 2 and x = 7 . Alternatively, using the quadratic formula also confirms these solutions. Both methods lead to the same answer, demonstrating the consistency in solving quadratic equations.
;

Answered by Anonymous | 2025-04-11