Translating the situation to a mathematical sentence, and solving, we find that the solutions are: [tex]x = 5 \pm 3\sqrt{2}[/tex]
The translation of the problem given is:
[tex](x - 5)^2 + 1 = 19[/tex]
Then, solving:
[tex](x - 5)^2 = 18[/tex]
[tex]x^2 - 10x + 25 = 18[/tex]
[tex]x^2 - 10x + 7 = 0[/tex]
Which is a quadratic equation with [tex]a = 1, b = -10, c = 7[/tex]. Then:
[tex]\Delta = (-10)^{2} - 4(1)(7) = 72[/tex]
[tex]x_{1} = \frac{-(10) + \sqrt{72}}{2}[/tex]
[tex]x_{2} = \frac{-(-10) - \sqrt{72}}{2}[/tex]
[tex]\sqrt{72} = \sqrt{9 \times 8} = \sqrt{3^2 \times 2^3} = 6\sqrt{2}[/tex], then:
[tex]x_1 = 5 + 3\sqrt{2}[/tex]
[tex]x_2 = 5 - 3\sqrt{2}[/tex]
The solutions are [tex]x = 5 \pm 3\sqrt{2}[/tex]
A similar problem is given at https://brainly.com/question/13094243
