By completing squares, we will see that the solutions of the quadratic equation are:
[tex]x = \pm \sqrt{23} + 9[/tex]
How to complete squares?
Here we need to remember that:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
Now we can start with the equation:
[tex]x^2 - 18x + 58 = 0[/tex]
We can rewrite this as:
[tex]x^2 - 2*9*x + 58 = 0[/tex]
Now we can add and subtract nine squared to get:
[tex]x^2 - 2*9*x + 81 - 81 + 58 = 0\\\\(x^2 - 2*9*x + 81) - 23 = 0\\\\(x - 9)^2 = 23[/tex]
So the two solutions are:
[tex]x = \pm \sqrt{23} + 9[/tex]
If you want to learn more about completing squares:
https://brainly.com/question/10449635
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