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Solve: x² - 4x + 85=0 A. {7+3i, 7 - 3i B. {2+9i, 2 – 91 c. {3+ 71,3 - 7i O D. {2+191,2 - 1911

1 Answer

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We are given the following equation:


x^(2)-4x+85=0

To solve for "x" we will use the quadratic formula, which is:


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

Where the values of "a", "b" and "c" are the coefficients of the equation:


ax^2+bx+c

Therefore, in this case, we have:


\begin{gathered} a=1 \\ b=-4 \\ c=85 \end{gathered}

Replacing in the quadratic formula:


x=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(85)}}{2(1)}

Solving the operations inside the radical:


x=\frac{-(-4)\pm\sqrt[]{-324}}{2}

Now we divide the number inside the radical a the product of -1 and 324:


x=\frac{-(-4)\pm\sqrt[]{(-1)(324)}}{2}

Now we divide the square root:


x=\frac{-(-4)\pm\sqrt[]{(-1)}\sqrt[]{324}}{2}

The square root of -1 is the imaginary unit "i". Therefore, solving the square roots we get:


x=(-(-4)\pm18i)/(2)

Now we separate the fraction:


x=(-(-4))/(2)\pm(18i)/(2)

Solving the operations:


x=2\pm9i

Therefore, the solutions of the equation are:


\begin{gathered} x_1=2+9i \\ x_2=2-9i \end{gathered}

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