Question

The sum of two times a number and its square is 80. What is/are the number(s)?

a) x = -10 or x = 8
b) x = -8 or x = 10
c) x = -9 or x = 9
d) x = -7 or x = 7

Answer 1

To find the number whose square added to twice the number equals 80, we derive the quadratic equation x² + 2x - 80 = 0, which factors into (x + 10)(x - 8) = 0, giving us the solutions x = -10 and x = 8.

Step-by-step explanation:

The question requires us to find a number whose square added to twice the number equals 80. This can be represented by a quadratic equation of the form x² + 2x = 80. First, we need to bring the equation to the standard quadratic form, which is ax² + bx + c = 0. We subtract 80 from both sides to get x² + 2x - 80 = 0.

Next, we can factor the quadratic equation, which splits into (x + 10)(x - 8) = 0. Setting each factor equal to zero gives us the solutions x = -10 and x = 8. Therefore, the numbers that satisfy the original equation are -10 and 8.