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+10x+21=0

Answer 1

To solve the equation x^2 + 10x + 21 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the general quadratic equation ax^2 + bx + c = 0.

In this case, a = 1, b = 10, and c = 21.

Next, we substitute these values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

Plugging in the values, we get:
x = (-10 ± √(10^2 - 4*1*21)) / 2*1
x = (-10 ± √(100 - 84)) / 2
x = (-10 ± √16) / 2
x = (-10 ± 4) / 2

This gives us two possible solutions:
x = (-10 + 4) / 2 = -6 / 2 = -3
x = (-10 - 4) / 2 = -14 / 2 = -7

Therefore, the solutions to the equation x^2 + 10x + 21 = 0 are x = -3 and x = -7.