Solve for \( x \):

\[ 2x^2 + 4x - 16 = 0 \]

in order to solve it, we need find the zero of the polynomial.
we find the zero of the polynomial by splitting the middle term method
2x2 -+ 4x - 16
= 2x2 + 8x - 4x -16
= 2x( x + 4)- 4(x + 4) = (2x-)(x+4)
we find the zeroes of the factors
experimentally we find two values, 2 and -4.
Thus, values of x are 2 and -4

Answered by tadvisohil886 | 2024-06-10

2 x 2 + 4 x − 16 = 0 / : 2 x 2 + 2 x − 8 = 0 ( ∗ ) x 2 + 2 x ⋅ 1 + 1 2 ​ ​ − 1 2 − 8 = 0 ( x + 1 ) 2 − 1 − 8 = 0 ( x + 1 ) 2 − 9 = 0 ( x + 1 ) 2 = 9 ⟺ x + 1 = − 3 or x + 1 = 3 x = − 3 − 1 or x = 3 − 1 x = − 4 or x = 2 ( ∗ ) ( a + b ) 2 = a 2 + 2 ab + b 2
0\ then\ x_1=\frac{-b-\sqrt\Delta}{2a}\ and\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=2^2-4\cdot1\cdot(-8)=4+32=36;\ \sqrt\Delta=\sqrt{36}=6\\\\x_1=\frac{-2-6}{2\cdot1}=\frac{-8}{2}=-4;\ x_2=\frac{-2+6}{2\cdot1}=\frac{4}{2}=2"> 2 x 2 + 4 x − 16 = 0 / : 2 x 2 + 2 x − 8 = 0 a = 1 ; b = 2 ; c = − 8 Δ = b 2 − 4 a c i f Δ > 0 t h e n x 1 ​ = 2 a − b − Δ ​ ​ an d x 2 ​ = 2 a − b + Δ ​ ​ Δ = 2 2 − 4 ⋅ 1 ⋅ ( − 8 ) = 4 + 32 = 36 ; Δ ​ = 36 ​ = 6 x 1 ​ = 2 ⋅ 1 − 2 − 6 ​ = 2 − 8 ​ = − 4 ; x 2 ​ = 2 ⋅ 1 − 2 + 6 ​ = 2 4 ​ = 2

Answered by Anonymous | 2024-06-24

To solve the quadratic equation 2 x 2 + 4 x − 16 = 0 , we simplify and use the quadratic formula. The solutions are x = 2 and x = − 4 .
;

Answered by tadvisohil886 | 2024-12-24