Solve the equation by factoring: 15x^(2)-50 x-x^(3)=0 Answer: x=

Rewrite in Standard Form: Rewrite the equation in standard form by arranging the terms in descending order of the powers of x. The equation is given as 15x^(2) - 50x - x^(3) = 0. We need to rearrange the terms to get x^(3) at the beginning. x^(3) - 15x^(2) + 50x = 0Factor Out Common Factor: Factor out the greatest common factor, which in this case is x. We can take x out from each term. x(x^(2) - 15x + 50) = 0Factor Quadratic Expression: Factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to 50 and add up to -15. These numbers are -5 and -10. x(x - 5)(x - 10) = 0Apply Zero-Product Property: Apply the zero-product property to find the solutions. If the product of several factors is zero, at least one of the factors must be zero. So, we set each factor equal to zero and solve for x. x = 0, x - 5 = 0, x - 10 = 0Solve for x: Solve each equation for x. From x = 0, we get x = 0. From x - 5 = 0, we get x = 5. From x - 10 = 0, we get x = 10.

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Q. Solve the equation by factoring:

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15 x^{2}-50 x-x^{3}=0

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Answer:

x=

Rewrite in Standard Form: Rewrite the equation in standard form by arranging the terms in descending order of the powers of $x$ . The equation is given as $15x^{2} - 50x - x^{3} = 0$ . We need to rearrange the terms to get $x^{3}$ at the beginning. $x^{3} - 15x^{2} + 50x = 0$
Factor Out Common Factor: Factor out the greatest common factor, which in this case is $x$ . We can take $x$ out from each term. $x(x^{2} - 15x + 50) = 0$
Factor Quadratic Expression: Factor the quadratic expression inside the parentheses. $\newline$ We need to find two numbers that multiply to $50$ and add up to $-15$ . These numbers are $-5$ and $-10$ . $\newline$ $x(x - 5)(x - 10) = 0$
Apply Zero-Product Property: Apply the zero-product property to find the solutions. $\newline$ If the product of several factors is zero, at least one of the factors must be zero. $\newline$ So, we set each factor equal to zero and solve for $x$ . $\newline$ $x = 0$ , $x - 5 = 0$ , $x - 10 = 0$
Solve for x: Solve each equation for x. $\newline$ From $x = 0$ , we get $x = 0$ . $\newline$ From $x - 5 = 0$ , we get $x = 5$ . $\newline$ From $x - 10 = 0$ , we get $x = 10$ .