Solve the equation for all values of x. -x(x^(2)-1)(49x^(2)-16) = 0 Answer: x =

Analyze the equation: Analyze the equation -x(x^2-1)(49x^2-16) = 0. We have a product of three terms equal to zero. According to the zero product property, if the product of several terms is zero, then at least one of the terms must be zero.Set each term: Set each term in the product equal to zero and solve for x. First term: -x = 0 Second term: x^2 - 1 = 0 Third term: 49x^2 - 16 = 0Solve first term: Solve the first term -x = 0. If -x = 0, then x = 0.Solve second term: Solve the second term x^2 - 1 = 0. Add 1 to both sides: x^2 = 1. Take the square root of both sides: x = ±1.Solve third term: Solve the third term 49x^2 - 16 = 0. This is a difference of squares, which can be factored as (7x - 4)(7x + 4) = 0. Set each factor equal to zero: 7x - 4 = 0 and 7x + 4 = 0.Solve 7x - 4: Solve 7x - 4 = 0. Add 4 to both sides: 7x = 4. Divide both sides by 7: x = 4/7.Solve 7x + 4: Solve 7x + 4 = 0. Subtract 4 from both sides: 7x = -4. Divide both sides by 7: x = -4/7.

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Q. Solve the equation for all values of

x

\newline

-x(x^{2}-1)(49x^{2}-16) = 0

\newline

Answer:

x =

Analyze the equation: Analyze the equation -x(x^\(2 $-1$ )( $49$ x^ $2$ $-16$ ) = $0$ ＂). $\newline$ We have a product of three terms equal to zero. According to the zero product property, if the product of several terms is zero, then at least one of the terms must be zero.
Set each term: Set each term in the product equal to zero and solve for $x$ . $\newline$ First term: $-x = 0$ $\newline$ Second term: $x^2 - 1 = 0$ $\newline$ Third term: $49x^2 - 16 = 0$
Solve first term: Solve the first term $-x = 0$ . $\newline$ If $-x = 0$ , then $x = 0$ .
Solve second term: Solve the second term $x^2 - 1 = 0$ . Add $1$ to both sides: $x^2 = 1$ . Take the square root of both sides: $x = \pm1$ .
Solve third term: Solve the third term $49x^2 - 16 = 0$ . This is a difference of squares, which can be factored as $(7x - 4)(7x + 4) = 0$ . Set each factor equal to zero: $7x - 4 = 0$ and $7x + 4 = 0$ .
Solve $7x - 4$ : Solve $7x - 4 = 0$ . $\newline$ Add $4$ to both sides: $7x = 4$ . $\newline$ Divide both sides by $7$ : $x = \frac{4}{7}$ .
Solve $7x + 4$ : Solve $7x + 4 = 0$ . $\newline$ Subtract $4$ from both sides: $7x = -4$ . $\newline$ Divide both sides by $7$ : $x = -\frac{4}{7}$ .