Answered

Solve x2 − 3x = −8.




x equals quantity of 3 plus or minus I square root of 29 all over 2



x equals quantity of 3 plus or minus I square root of 23 all over 2



x equals quantity of negative 3 plus or minus I square root of 29 all over 2



x equals quantity of negative 3 plus or minus I square root of 23 all over 2

Verified Answer :

calculista

we have

\(x^{2} -3x=-8\)

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

\(x^{2} -3x+1.5^{2}=-8+1.5^{2}\)

\(x^{2} -3x+1.5^{2}=-5.75\)

Rewrite as perfect squares

\((x-1.5)^{2}=-5.75\)

Square Root both sides

\(x-1.5=(+/-)\sqrt{-5.75}\)

Remember that

\(\sqrt{-1}=i\)

\(\sqrt{5.75}= \sqrt{\frac{23}{4}}=\frac{\sqrt{23}}{2}\)

Substitute

\(x-1.5=(+/-)i\frac{\sqrt{23}}{2}\)

\(x=1.5(+/-)i\frac{\sqrt{23}}{2}\)

\(x=(3/2)(+/-)i\frac{\sqrt{23}}{2}\)

\(x=(3/2)+i\frac{\sqrt{23}}{2}=\frac{3+i\sqrt{23}}{2}\)

\(x=(3/2)-i\frac{\sqrt{23}}{2}=\frac{3-i\sqrt{23}}{2}\)

therefore

the answer is

x equals quantity of 3 plus or minus I square root of 23 all over 2

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