Using it's formula, the solutions to the quadratic equation x² - 8x + 16 = 11 are: [tex]x = -4 \pm \sqrt{11}[/tex]
A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
In this problem, the equation is:
x² - 8x + 16 = 11
In standard-form:
x² - 8x + 5 = 0
The coefficients are a = 1, b = -8, c = 5, hence:
[tex]\Delta = (-8)^2 - 4(1)(5) = 44[/tex]
[tex]x_1 = \frac{-8 + \sqrt{44}}{2} = -4 + \sqrt{11}[/tex]
[tex]x_2 = \frac{-8 - \sqrt{44}}{2} = -4 - \sqrt{11}[/tex]
More can be learned about quadratic equations at https://brainly.com/question/24737967
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