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Use the quadratic formula to solve the equation. (Round to two decimal places.) x²-2x-15-0

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Final answer:

The quadratic equation x²-2x-15=0 is solved using the quadratic formula, resulting in two solutions: x = 5 and x = -7.5.

Step-by-step explanation:

The student is attempting to solve a quadratic equation, specifically x²-2x-15=0, using the quadratic formula. To apply the quadratic formula, we must recognize the general form of a quadratic equation as ax²+bx+c=0, where 'a', 'b', and 'c' are coefficients. In our case, a=1, b=-2, and c=-15. The quadratic formula is given by x = (-b ± √(b²-4ac)) / (2a).

Substituting our coefficients into the formula provides us two solutions:

  1. x = (-(-2) ± √((-2)²-4(1)(-15))) / (2(1))
  2. x = (2 ± √(4+60)) / 2
  3. x = (2 ± √64) / 2
  4. x = (2 ± 8) / 2
  5. Our possible solutions for x are therefore 5 and -7.5.

Confirming this, we would get x = 5 and x = -7.5 as the solutions for the given quadratic equation, rounded to two decimal places as instructed.

User FirebladeDan
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