thomasjordan99
Answered

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Need to know this now pls !!! NEED THE PROCESS , TOO!!!

x squared - 18x = -117

Sagot :

Abu99

Answer:

x = 9 + 6i or x = 9 - 6i

Step-by-step explanation:

x² - 18x + 117 = 0

Complete the square and solve:

(x - 9)² - 81 + 117 = 0

(x - 9)² + 36 = 0

(x - 9)² = -36

x - 9 = ±sqrt(-36)

x - 9 = ±sqrt(-1).sqrt(36)

i = imaginary number = sqrt(-1)

x - 9 = ±6i

x = 9 ± 6i

There are no real solutions, only imaginary ones

9 + 6i and 9 - 6i

Answer:

[tex]x_1=9+6i[/tex]

[tex]x_2=9-6i[/tex]

Step-by-step explanation:

Given:

[tex]x^2-18x=-117[/tex]

Rewrite as a quadratic equation:

[tex]x^2-18x+117=0[/tex]

Use the quadratic formula:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x=\frac{-(-18)\pm\sqrt{(-18)^2-4(1)(117)}}{2(1)}[/tex]

[tex]x=\frac{18\pm\sqrt{324-468}}{2}[/tex]

[tex]x=\frac{18\pm\sqrt{-144}}{2}[/tex] <-- No real solutions since discriminant is negative

Continuation:

[tex]x=\frac{18\pm\sqrt{-1*144}}{2}[/tex]

[tex]x=\frac{18\pm\sqrt{-1}\sqrt{144}}{2}[/tex]

[tex]x=\frac{18\pm12i}{2}[/tex] <-- Recall that [tex]\sqrt{-1}=i[/tex]

[tex]x=9\pm6i[/tex]

Solutions:

[tex]x_1=9+6i[/tex]

[tex]x_2=9-6i[/tex]

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