Question

What is the positive solution to the equation 0 equals negative x squared plus 2 x plus 1

Answer 1

The positive solution to the quadratic equation 0 = -x² + 2x + 1 is found by applying the quadratic formula, resulting in x = √2 - 1.

Step-by-step explanation:

The positive solution to the equation 0 = -x² + 2x + 1 can be found using the quadratic formula, which is applicable for equations of the form ax² + bx + c = 0. The quadratic formula is given by x = (-b ± √(b² - 4ac))/(2a). Let's identify a, b, and c from the given equation: a = -1, b = 2, and c = 1.

By substituting these values into the quadratic formula, we calculate:

x = (-2 ± √((2)² - 4(-1)(1)))/ (2*(-1))
x = (-2 ± √(4 + 4))/(-2)
x = (-2 ± √(8))/(-2)
x = (-2 ± 2√2)/(-2)

Now we evaluate both possible solutions:

x = (-2 + 2√2)/(-2)

x = (-2 - 2√2)/(-2)

The first solution gives us the positive value for x, and the second gives the negative value for x. Since we are looking only for the positive solution, we discard the negative one.

Thus, the positive solution is: x = (2√2 - 2)/2 or simplified x = √2 - 1.

Answer 2

The solution is x=1. This video can give you a better explanation of quadratics than I can. If you look up solving quadratics on youtube, it could probably give you a better explanation than I can. Anyways, I worked out the problem using the x method to find its factors, which turned out to be -1. In factored form, the equation is (x-1)(x-1)=0. When x=1, the equation will equal 0.