Answer: x = \(\frac{7±i\sqrt{3}}{2}\) (Ignore the A)
Step-by-step explanation: This is step-by-step using the QF (quadratic formula)
The first step is putting it into SF (Standard Form). Keep in mind the formula for SF is \(ax^{2}\) ± \(bx\) ± c= 0.
You will want to move the -13 from the right side to the left by subtracting it.
x2 – 7x = –13
+13 +13 (in order to cancel out -13 you will need to use the
--------------------------- opposite operation, in this case adding it.) You will get
\(x^{2}\) - 7x + 13= 0 Now you want to use the QF, which is \(\frac{-b+/- \sqrt{b^{2} -4ac} }{2a}\)
a = 1 (remember that \(x^{2}\) has an invisible 1 in front of it) b = -7 (don"t forget any negative signs with the number(s)) c = 13
\(x=\frac{-(-7)+/-\sqrt{(-7)^{2}-4(1)(13) } }{2(1)}\) Put everything in parenthesis to make it easier.
Use PEMDAS to solve. Start with \((-7)^{2}\)
\(x = \frac{-(-7)+/-\sqrt{49-4(1)(13)} }{2(1)}\) Now do all the multiplication under the square root first. Then the -(-7) and lastly the 2(1).
\(x=\frac{7+/-\sqrt{49-52} }{2}\) (1x13=13 and 4x13= 52) Now do the math in the square root.
\(x=\frac{7+/-\sqrt{-3} }{2}\) --- \(x=\frac{7+/-\sqrt{-1}* \sqrt{3} }{2}\) ---- \(x=\frac{7+/-i \sqrt{3} }{2}\) There's your answer.
Remember because \(\sqrt{-3}\) is not a real number it has to be broken down into \(\sqrt{-1} *\sqrt{3}\). -1 is = to i. i stands for imagiary.
