Solve for all values of x : 4x^(2)(x-10)-(x-10)=0 Answer: x=

Factor out common term: Factor out the common term (x-10) from the equation. The equation is 4x^2(x-10) - (x-10) = 0. We can factor (x-10) out of both terms. (x-10)(4x^2 - 1) = 0Set first factor equal: Set each factor equal to zero and solve for x. First, set the first factor equal to zero: x - 10 = 0 x = 10Set second factor equal: Set the second factor equal to zero and solve for x. 4x^2 - 1 = 0 This is a difference of squares and can be factored further: (2x - 1)(2x + 1) = 0Factor difference of squares: Set each factor of the difference of squares equal to zero and solve for x. First, set the first factor equal to zero: 2x - 1 = 0 2x = 1 x = 1/2Solve for x: Set the second factor equal to zero and solve for x. 2x + 1 = 0 2x = -1 x = -1/2

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Solve for all values of
x :

4x^(2)(x-10)-(x-10)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $4 x^{2}(x-10)-(x-10)=0$ $\newline$ Answer: $x=$

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Algebra 2

Composition of linear and quadratic functions: find a value

Full solution

Q. Solve for all values of

x

\newline

4 x^{2}(x-10)-(x-10)=0

\newline

Answer:

x=

Factor out common term: Factor out the common term $(x-10)$ from the equation. $\newline$ The equation is $4x^2(x-10) - (x-10) = 0$ . We can factor $(x-10)$ out of both terms. $\newline$ $(x-10)(4x^2 - 1) = 0$
Set first factor equal: Set each factor equal to zero and solve for $x$ . $\newline$ First, set the first factor equal to zero: $\newline$ $x - 10 = 0$ $\newline$ $x = 10$
Set second factor equal: Set the second factor equal to zero and solve for $x$ . $4x^2 - 1 = 0$ This is a difference of squares and can be factored further: $(2x - 1)(2x + 1) = 0$
Factor difference of squares: Set each factor of the difference of squares equal to zero and solve for $x$ . $\newline$ First, set the first factor equal to zero: $\newline$ $2x - 1 = 0$ $\newline$ $2x = 1$ $\newline$ $x = \frac{1}{2}$
Solve for x: Set the second factor equal to zero and solve for x. $\newline$ $2x + 1 = 0$ $\newline$ $2x = -1$ $\newline$ $x = -\frac{1}{2}$