Question

Solve.

Answer 1

Translating the situation to a mathematical sentence, and solving, we find that the solutions are: $x = 5 \pm 3\sqrt{2}$

The translation of the problem given is:

$(x - 5)^2 + 1 = 19$

Then, solving:

$(x - 5)^2 = 18$

$x^2 - 10x + 25 = 18$

$x^2 - 10x + 7 = 0$

Which is a quadratic equation with $a = 1, b = -10, c = 7$. Then:

$\Delta = (-10)^{2} - 4(1)(7) = 72$

$x_{1} = \frac{-(10) + \sqrt{72}}{2}$

$x_{2} = \frac{-(-10) - \sqrt{72}}{2}$  

$\sqrt{72} = \sqrt{9 \times 8} = \sqrt{3^2 \times 2^3} = 6\sqrt{2}$, then:

$x_1 = 5 + 3\sqrt{2}$

$x_2 = 5 - 3\sqrt{2}$

The solutions are $x = 5 \pm 3\sqrt{2}$

A similar problem is given at brainly.com/question/13094243