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(ii) the values of
x when
5+4x-x^(2)=0,

(ii) the values of $x$ when $5+4 x-x^{2}=0$ ,

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Solve complex trigonomentric equations

Full solution

Q. (ii) the values of

x

when

5+4 x-x^{2}=0

,

Write Equation: Write down the given quadratic equation. $\newline$ The given equation is $5 + 4x - x^2 = 0$ . We need to find the values of $x$ that satisfy this equation.
Standard Form: Rearrange the equation in standard quadratic form. $\newline$ To solve the quadratic equation, we need to write it in the form $ax^2 + bx + c = 0$ . In this case, we need to rearrange the terms to get $-x^2 + 4x + 5 = 0$ .
Multiply by $-1$ : Multiply the entire equation by $-1$ to make the $x^2$ term positive. $\newline$ Multiplying by $-1$ , we get $x^2 - 4x - 5 = 0$ . This is now in standard form.
Factor Equation: Factor the quadratic equation. $\newline$ We need to find two numbers that multiply to $-5$ and add up to $-4$ . The numbers that satisfy these conditions are $-5$ and $1$ . So we can factor the equation as $(x - 5)(x + 1) = 0$ .
Set Equal and Solve: Set each factor equal to zero and solve for $x$ . Setting each factor equal to zero gives us two equations: $x - 5 = 0$ and $x + 1 = 0$ . Solving these equations gives us $x = 5$ and $x = -1$ .

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