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Solve the equation 4x2−25=04x^2 - 25 = 0.

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Full solution

Q. Solve the equation 4x2−25=04x^2 - 25 = 0.
  1. Recognize as difference of squares: Recognize the equation 4x2−25=04x^2 - 25 = 0 as a difference of squares.\newlineThe equation can be factored as (2x+5)(2x−5)=0(2x + 5)(2x - 5) = 0.
  2. Set factors equal to zero: Set each factor equal to zero to find the solutions for xx.\newlineFirst factor: 2x+5=02x + 5 = 0\newlineSecond factor: 2x−5=02x - 5 = 0
  3. Solve for x: Solve the first factor for x.\newline2x+5=02x + 5 = 0\newlineSubtract 55 from both sides: 2x=−52x = -5\newlineDivide both sides by 22: x=−52x = -\frac{5}{2}
  4. Solve for x: Solve the second factor for x.\newline2x−5=02x - 5 = 0\newlineAdd 55 to both sides: 2x=52x = 5\newlineDivide both sides by 22: x=52x = \frac{5}{2}

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