Solve the value of x if y=-2x^2 +2x +16 ?

To solve for the value of x, we need to set y equal to the given equation and then solve for x.

Given: y = -2x^2 + 2x + 16

Now, let y = 0 (since we are solving for x)

0 = -2x^2 + 2x + 16

Now, we need to solve this quadratic equation for x. We can do this by factoring, completing the square, or using the quadratic formula.

Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -2, b = 2, and c = 16.

x = (-2 ± √(2^2 - 4(-2)(16))) / 2(-2)
x = (-2 ± √(4 + 128)) / -4
x = (-2 ± √132) / -4
x = (-2 ± 11.49) / -4

Now, we have two possible solutions for x:

x = (-2 + 11.49) / -4 = 9.49 / -4 = -2.3725

x = (-2 - 11.49) / -4 = -13.49 / -4 = 3.3725

Therefore, the values of x are approximately -2.3725 and 3.3725.

y=-2x^2 + 2x + 16

The equation is in the form of a quadratic equation: y = ax^2 + bx + c

In this case, a = -2, b = 2, and c = 16

Using the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a

x = (-2 ± sqrt(2^2 - 4(-2)(16))) / 2(-2)

x = (-2 ± sqrt(68)) / -4

x = (-2 ± 2.60) / -4

x = -1/2 or x = 4