Question

Solve the following quadratic equation using the quadratic formula. Separate multiple answers with a comma if necessary.

y2+7y−2=0

Answer 1

The quadratic equation y2 + 7y - 2 = 0 can be solved using the quadratic formula, which states that the solutions for x in the equation ax^2 + bx + c = 0 are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

We can apply the quadratic formula to this equation by letting a = 1, b = 7, and c = -2:

y = (-7 ± √(7^2 - 4 * 1 * -2)) / 2 * 1

y = (-7 ± √(49 + 8)) / 2

y = (-7 ± √57) / 2

So the solutions to the equation y2 + 7y - 2 = 0 are:

y = (-7 + √57) / 2

y = (-7 - √57) / 2

The solutions to the equation are y = (-7 + √57) / 2 and y = (-7 - √57) / 2.