The quadratic formula is: (-b +- sqrt(b^2 - 4ac))/(2a), Therefore the first step is to identify a,b & c. We need to ensure that the equation is =0 and in this case that is true.
Then we are able to obtain the values to substitute into the formula; the general quadratic formula layout is ax^2 + bx +c therefore we look at your equation: x^2 - 6x + 6. The value of a has to be 1 since x^2 is multiplied by 1. Then b = -6, maintaining the negative is essential to the calculation (the sign will also stay with the value that is next in the equation). Then c = 6.
We now substitute a= 1, b=-6 and c= 6 into the quadratic formula.
x = (-b +- sqrt(b^2 - 4ac))/(2a) = (-(-6) +- sqrt((-6)^2 - 4(1)(6)))/(2(1))
Now that we have the values substituted into the equation we first solve the inside of the square root. So,
x = (-(-6) +- sqrt(12))/(2(1))
Since the value under the root (discriminant) is positive we know that there will be two real solutions for x.
Separate the two x values so that we solve for the positive root first.
x_1 = (-(-6) + sqrt(12))/(2(1)) = 4.73 (3 sf)
Now solve the second x value by using the negative root.
x_2 = (-(-6) - sqrt(12))/(2(1)) = 1.27 (3 sf)
