Solve for all values of x : x^(2)(2x-9)+13 x(2x-9)+40(2x-9)=0 Answer: x=

Factor out common term: First, notice that the term (2x-9) is common in all three parts of the equation. Factor out (2x-9). x^2(2x-9) + 13x(2x-9) + 40(2x-9) = 0 (2x-9)(x^2 + 13x + 40) = 0Factor quadratic expression: Next, we need to factor the quadratic expression x^2 + 13x + 40. x^2 + 13x + 40 can be factored into (x + 5)(x + 8) because 5 * 8 = 40 and 5 + 8 = 13. So, (2x-9)(x^2 + 13x + 40) becomes (2x-9)(x + 5)(x + 8) = 0Apply zero product property: Now, we have a product of three factors equal to zero. According to the zero product property, 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: 2x - 9 = 0 x + 5 = 0 x + 8 = 0Solve for x: Solve the first equation for x: 2x - 9 = 0 2x = 9 x = 9/2 x = 4.5Solve for x: Solve the second equation for x: x + 5 = 0 x = -5Solve for x: Solve the third equation for x: x + 8 = 0 x = -8

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Solve for all values of
x :

x^(2)(2x-9)+13 x(2x-9)+40(2x-9)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $x^{2}(2 x-9)+13 x(2 x-9)+40(2 x-9)=0$ $\newline$ Answer: $x=$

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Algebra 1

Solve linear equations: mixed review

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Q. Solve for all values of

x

\newline

x^{2}(2 x-9)+13 x(2 x-9)+40(2 x-9)=0

\newline

Answer:

x=

Factor out common term: First, notice that the term $(2x-9)$ is common in all three parts of the equation. Factor out $(2x-9)$ . $x^2(2x-9) + 13x(2x-9) + 40(2x-9) = 0$ $(2x-9)(x^2 + 13x + 40) = 0$
Factor quadratic expression: Next, we need to factor the quadratic expression $x^2 + 13x + 40$ . $x^2 + 13x + 40$ can be factored into $(x + 5)(x + 8)$ because $5 \times 8 = 40$ and $5 + 8 = 13$ . So, $(2x-9)(x^2 + 13x + 40)$ becomes $(2x-9)(x + 5)(x + 8) = 0$
Apply zero product property: Now, we have a product of three factors equal to zero. According to the zero product property, 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 $x$ : $\newline$ $2x - 9 = 0$ $\newline$ $x + 5 = 0$ $\newline$ $x + 8 = 0$
Solve for x: Solve the first equation for x: $\newline$ $2x - 9 = 0$ $\newline$ $2x = 9$ $\newline$ $x = \frac{9}{2}$ $\newline$ $x = 4.5$
Solve for x: Solve the second equation for x: $\newline$ $x + 5 = 0$ $\newline$ $x = -5$
Solve for x: Solve the third equation for x: $\newline$ $x + 8 = 0$ $\newline$ $x = -8$