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What are the solutions of this quadratic equation? x2 − 18x + 58 = 0 A. B. C. D.

Sagot :

altavistard

Answer:

Step-by-step explanation:

Let's use "completing the square" to solve this quadratic:  x^2 − 18x + 58 = 0

We want to rewrite the terms "x^2 - 18x" in the form '(x - h)^2 - h^2 and leave the terms '58 = 0' as they are:

Taking half of the coefficient of x (which coefficient is -18), we get -9.  We square this -9, obtaining 81, and then rewrite

"x^2 - 18x"   as  "x^2 - 18x" + 81 - 81."  To this we must append '58 = 0":

x^2 - 18x + 81 - 81 + 58, or x^2 - 18x + 81 - 23 = 0

Now the first three terms condense to the expression

(x - 9)^2, which is then followed by "-23":

(x - 9)^2 = 23

Solve this for x.  Taking the square root of both sides, we get

x - 9 = ± √23

so that one root is x = 9 + √23

and the other is x = 9 - √23

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