Solve the equation by factoring: 34x^(2)-140 x-2x^(3)=0 Answer: x=

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Solve the equation by factoring:  34x^(2)-140 x-2x^(3)=0 Answer:  x=

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Rewrite Equation in Standard Form: Rewrite the equation in standard form. To solve the equation by factoring, we first need to rewrite the equation in standard form, which means the terms should be ordered from the highest power to the lowest power of x. The given equation is 34x^2 - 140x - 2x^3 = 0. We need to rearrange the terms to get the cubic term first. The standard form of the equation is -2x^3 + 34x^2 - 140x = 0.Factor Out Common Factor: Factor out the greatest common factor. We can see that each term in the equation has a factor of x. We will factor out the greatest common factor, which is x. The factored equation is x(-2x^2 + 34x - 140) = 0.Factor Quadratic Expression: Factor the quadratic expression. Now we need to factor the quadratic expression -2x^2 + 34x - 140. To do this, we look for two numbers that multiply to -2 * -140 = 280 and add up to 34. The numbers that satisfy these conditions are 40 and -7. We can rewrite the quadratic expression as -2x^2 + 40x - 7x - 140.Group and Factor by Grouping: Group the terms and factor by grouping. We group the terms to factor by grouping: (-2x^2 + 40x) + (-7x - 140). Now we factor out the common factors from each group: 2x(-x + 20) - 7(-x - 20).Factor Out Common Binomial Factor: Factor out the common binomial factor. We notice that both groups have a common binomial factor of (-x + 20). The fully factored form of the quadratic expression is (2x - 7)(-x + 20).Write Fully Factored Form: Write the fully factored form of the original equation. Now we combine the factored quadratic expression with the x we factored out in Step 2. The fully factored form of the original equation is x(2x - 7)(-x + 20) = 0.Solve for x: Solve for x by setting each factor equal to zero. To find the solutions, we set each factor equal to zero and solve for x. x = 0, 2x - 7 = 0, and -x + 20 = 0. Solving each equation gives us the solutions: x = 0, x = 7/2, and x = 20.

Solve the equation by factoring: $\newline$ $34 x^{2}-140 x-2 x^{3}=0$ $\newline$ Answer: $x=$

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Solve the equation by factoring:\newline34x2−140x−2x3=0 34 x^{2}-140 x-2 x^{3}=0 34x2−140x−2x3=0\newlineAnswer: x= x= x=

Solve the equation by factoring: $\newline$ $34 x^{2}-140 x-2 x^{3}=0$ $\newline$ Answer: $x=$