Suppose you are a solving a quadratic equation using the quadratic formula and this is your work so far:%0D%0A%0D%0A 2x2+7x−15=0%0D%0A%0D%0A%0D%0A%0D%0Ax=%0D%0A−7 ±72−42−15%0D%0A22%E2%80%8B%0D%0A%0D%0A%0D%0A%0D%0Ax=%0D%0A−7 ±???%0D%0A4%E2%80%8B👈
To continue solving the quadratic equation 2x^2 + 7x - 15 = 0 using the quadratic formula, we need to calculate the discriminant first:
Discriminant (Δ) = b^2 - 4ac
where a = 2, b = 7, and c = -15
Plugging the values in:
Δ = 7^2 - 4(2)(-15)
Δ = 49 + 120
Δ = 169
Now that we have the discriminant, we can substitute the values into the quadratic formula:
x = (-7 ± √Δ) / 2(2)
x = (-7 ± √169) / 4
x = (-7 ± 13) / 4
Now we have two possible solutions:
x = (-7 + 13) / 4 = 6 / 4 = 1.5
x = (-7 - 13) / 4 = -20 / 4 = -5
Therefore, the solutions to the quadratic equation 2x^2 + 7x - 15 = 0 are x = 1.5 and x = -5.