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Crazy boy [7]
3 years ago
11

Solve x2 – 7x = –13.

Mathematics
2 answers:
vampirchik [111]3 years ago
8 0
This results in a non-real solution X= 7/2 + i (sqrt 3)/2 and x= 7/2 - i (sqrt 3)/2
aleksklad [387]3 years ago
6 0

we have

x^{2} -7x=-13

Complete the square. Remember to balance the equation by adding the same constants to each side

x^{2} -7x+3.5^{2}=-13+3.5^{2}

x^{2} -7x+12.25=-13+12.25

x^{2} -7x+12.25=-0.75

Rewrite as perfect squares

(x-3.5)^{2}=-0.75

remember that

i=\sqrt{-1}

Square root both sides

(x-3.5)=(+/-)\sqrt{-0.75}

(x-3.5)=(+/-)\sqrt{-1*0.75}

(x-3.5)=(+/-)\sqrt{0.75}i

x1=3.5+\sqrt{0.75}i

x2=3.5-\sqrt{0.75}i

Simplify

\sqrt{0.75}=\frac{\sqrt{3}}{2}

x1=3.5+\frac{\sqrt{3}}{2}i

x2=3.5-\frac{\sqrt{3}}{2}i

therefore

<u>the answer is</u>

x1=3.5+\frac{\sqrt{3}}{2}i

x2=3.5-\frac{\sqrt{3}}{2}i

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