Question
Solve using the quadratic formula Write your answers as integers proper or improper fractions in simplest form or decimals rounded to the nearest hundredth
x^2-5x-14=0
x^2-5x-14=0
Answers
GPT 3.5
To solve the quadratic equation x^2 - 5x - 14 = 0 using the quadratic formula, we first identify the coefficients a, b, and c in the general quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = -5, and c = -14.
Now we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (5 ± √((-5)^2 - 4(1)(-14))) / 2(1)
x = (5 ± √(25 + 56)) / 2
x = (5 ± √81) / 2
x = (5 ± 9) / 2
Now we have two possible solutions:
x = (5 + 9) / 2 = 14 / 2 = 7
x = (5 - 9) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x^2 - 5x - 14 = 0 are x = 7 and x = -2.
In this case, a = 1, b = -5, and c = -14.
Now we can apply the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (5 ± √((-5)^2 - 4(1)(-14))) / 2(1)
x = (5 ± √(25 + 56)) / 2
x = (5 ± √81) / 2
x = (5 ± 9) / 2
Now we have two possible solutions:
x = (5 + 9) / 2 = 14 / 2 = 7
x = (5 - 9) / 2 = -4 / 2 = -2
Therefore, the solutions to the equation x^2 - 5x - 14 = 0 are x = 7 and x = -2.