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Solve the equation $4x^2 - 25 = 0$ .

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Determine the direction of a vector scalar multiple

Full solution

Q. Solve the equation

4x^2 - 25 = 0

.

Recognize as difference of squares: Recognize the equation $4x^2 - 25 = 0$ as a difference of squares. $\newline$ The equation can be factored as $(2x + 5)(2x - 5) = 0$ .
Set factors equal to zero: Set each factor equal to zero to find the solutions for $x$ . $\newline$ First factor: $2x + 5 = 0$ $\newline$ Second factor: $2x - 5 = 0$
Solve for x: Solve the first factor for x. $\newline$ $2x + 5 = 0$ $\newline$ Subtract $5$ from both sides: $2x = -5$ $\newline$ Divide both sides by $2$ : $x = -\frac{5}{2}$
Solve for x: Solve the second factor for x. $\newline$ $2x - 5 = 0$ $\newline$ Add $5$ to both sides: $2x = 5$ $\newline$ Divide both sides by $2$ : $x = \frac{5}{2}$

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