Solve the equation 3, x, squared, minus, 16, x, plus, 3, equals, 03x 2 −16x+3=0 to the nearest tenth.

The given equation is a quadratic equation of the form ax^2 + bx + c = 0. The general solution for such an equation is given by the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here, a = 3, b = -16, and c = 3.

Step 1: Calculate the value under the square root in the quadratic formula, which is b^2 - 4ac. = (-16)^2 - 433 = 256 - 36 = 220

Step 2: Calculate the values of x using the quadratic formula. x = [16 ± sqrt(220)] / (2*3)

So, the solutions are:

x1 = [16 + sqrt(220)] / 6 x2 = [16 - sqrt(220)] / 6

Using a calculator, we find that sqrt(220) is approximately 14.832.

So,

x1 = [16 + 14.832] / 6 ≈ 5.1 x2 = [16 - 14.832] / 6 ≈ 0.2

So, the solutions to the equation 3x^2 - 16x + 3 = 0 to the nearest tenth are x = 5.1 and x = 0.2.