Solve for all values of x : 25x^(2)(5x+7)-16(5x+7)=0 Answer: x=

Factor Out Common Term: Factor out the common term (5x+7) from the equation. Given equation: 25x^(2)(5x+7)-16(5x+7)=0 We can factor (5x+7) out of both terms: (5x+7)(25x^2 - 16) = 0Set Equations Equal: Set each factor equal to zero and solve for x. We have two factors: (5x+7) and (25x^2 - 16). Setting each equal to zero gives us two separate equations to solve: 1) 5x+7 = 0 2) 25x^2 - 16 = 0Solve 5x+7=0: Solve the first equation 5x+7 = 0 for x. Subtract 7 from both sides: 5x = -7 Divide by 5: x = -7/5Solve 25x^2-16=0: Solve the second equation 25x^2 - 16 = 0 for x. This is a difference of squares, which can be factored as: (5x - 4)(5x + 4) = 0 Set each factor equal to zero: 5x - 4 = 0 or 5x + 4 = 0Solve 5x-4=0: Solve the equation 5x - 4 = 0 for x. Add 4 to both sides: 5x = 4 Divide by 5: x = 4/5Solve 5x+4=0: Solve the equation 5x + 4 = 0 for x. Subtract 4 from both sides: 5x = -4 Divide by 5: x = -4/5

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Solve for all values of
x :

25x^(2)(5x+7)-16(5x+7)=0
Answer:
x=

Solve for all values of $x$ : $\newline$ $25 x^{2}(5 x+7)-16(5 x+7)=0$ $\newline$ Answer: $x=$

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Algebra 2

Solve complex trigonomentric equations

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Q. Solve for all values of

x

\newline

25 x^{2}(5 x+7)-16(5 x+7)=0

\newline

Answer:

x=

Factor Out Common Term: Factor out the common term $(5x+7)$ from the equation. $\newline$ Given equation: $25x^{2}(5x+7)-16(5x+7)=0$ $\newline$ We can factor $(5x+7)$ out of both terms: $\newline$ $(5x+7)(25x^2 - 16) = 0$
Set Equations Equal: Set each factor equal to zero and solve for $x$ . We have two factors: $(5x+7)$ and $(25x^2 - 16)$ . Setting each equal to zero gives us two separate equations to solve: $1$ ) $5x+7 = 0$ $2$ ) $25x^2 - 16 = 0$
Solve $5x+7=0$ : Solve the first equation $5x+7 = 0$ for $x$ . $\newline$ Subtract $7$ from both sides: $\newline$ $5x = -7$ $\newline$ Divide by $5$ : $\newline$ $x = -\frac{7}{5}$
Solve $25x^2-16=0$ : Solve the second equation $25x^2 - 16 = 0$ for $x$ . This is a difference of squares, which can be factored as: $(5x - 4)(5x + 4) = 0$ Set each factor equal to zero: $5x - 4 = 0$ or $5x + 4 = 0$
Solve $5x-4=0$ : Solve the equation $5x - 4 = 0$ for $x$ . $\newline$ Add $4$ to both sides: $\newline$ $5x = 4$ $\newline$ Divide by $5$ : $\newline$ $x = \frac{4}{5}$
Solve $5x+4=0$ : Solve the equation $5x + 4 = 0$ for $x$ . $\newline$ Subtract $4$ from both sides: $\newline$ $5x = -4$ $\newline$ Divide by $5$ : $\newline$ $x = -\frac{4}{5}$