If \( 2x^2 + 6x = 36 \), what are the possible values of \( x \)?

f(x) = 2(x + 3)(x - 6) ;

Answered by jaccusdarrisaw55 | 2024-06-12

The possible values of x for 2 ⋅ x 2 + 6 ⋅ x = 36 are x 1 ​ = 3 and x 2 ​ = − 6 .
The expression 2 ⋅ x 2 + 6 ⋅ x = 36 is equivalent to the expression 2 ⋅ x 2 + 6 ⋅ x − 36 = 0 , which represents a second order polynomial , that is, a polynomial of the form:
y = a ⋅ x 2 + b ⋅ x + c (1)
Where a , b , c are coefficients .
The possible values of x represents all possible roots of x, which are found analytically by the quadratic formula :
x = 2 ⋅ a − b ± b 2 − 4 ⋅ a ⋅ c ​ ​ (2)
If we know that a = 2 , b = 6 and c = − 36 , then all possible values of x are, respectively:
x 1 ​ = 3 , x 2 ​ = − 6
The possible values of x for 2 ⋅ x 2 + 6 ⋅ x = 36 are x 1 ​ = 3 and x 2 ​ = − 6 .
We kindly invite to check this question on second order polynomials : https://brainly.com/question/24356198

Answered by xero099 | 2024-06-15

The possible values of x for the equation 2 x 2 + 6 x = 36 are x = 3 and x = − 6 . This was determined by rearranging the equation into standard quadratic form and applying the quadratic formula. By solving, we found two roots: 3 and − 6 .
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Answered by xero099 | 2024-09-26