The solution for the given expression is: [tex]\frac{-1+ i*\sqrt{19} }{2}[/tex] and [tex]\frac{-1- i*\sqrt{19} }{2}[/tex].
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
For solving a quadratic function you should find the discriminant: D=b²-4ac and after that use this variable in the formula: [tex]x=\frac{-b\pm \sqrt{D} }{2a}[/tex]
Properties of Multiplication
The properties of multiplication are:
- Distributive: a(b±c)= ab±ac
- Comutative: a . b = b. a
- Associative: a(b+c)= c(a+b)
- Identity: b.1=b
Here, you should apply the distributive property for solving this expression.
x*(2x)+2*(x+5) = 2x²+2x+10
After that, you should solve the previous quadratic equation.
D=b²-4ac=4-4*2*10=4-80= -76
Then,
[tex]x_{1,2}=\frac{-2\pm \sqrt{-76} }{2*2}=\frac{-2\pm i*\sqrt{76} }{4}=\frac{-2\pm i*2\sqrt{19} }{4}=\frac{-1\pm i*\sqrt{19} }{2}[/tex]
Read more about the quadratic function here:
brainly.com/question/1497716
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