Question

Solve using the quadratic formula.
•Show all work.
•Write each solution in simplest form.
•No decimals.​

Answer 1

$\tt \: x ^ { 2 } +2x+7=0$

All equations of the form $\tt \: ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\tt \: \frac{-b±\sqrt{b^{2}-4ac}}{2a}$

The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$\tt \: x^{2}+2x+7=0$

This equation is in standard form: $\tt \: ax^{2}+bx+c=0$Substitute 1 for a, 2 for b, and 7 for c in the quadratic formula, $\tt \: \frac{-b±\sqrt{b^{2}-4ac}}{2a}$

$\tt \: x=\frac{-2±\sqrt{2^{2}-4\times 7}}{2} \\ \\ \tt \: x=\frac{-2±\sqrt{4-4\times 7}}{2} \\ \\ \tt \: x=\frac{-2±\sqrt{4-28}}{2} \\ \\ \tt \: x=\frac{-2±\sqrt{-24}}{2}$

$\tt \: x=\frac{-2±2\sqrt{6}i}{2}$

Now solve the equation $\tt \: x=\frac{-2±2\sqrt{6}i}{2}$ when ± is plus. Add $\tt \: -2 \: to \: 2i\sqrt{6}$

$\tt \: x=\frac{-2+2\sqrt{6}i}{2}$

Divide $\tt \: -2+2i\sqrt{6}$ by 2.

$\sf \: x=-1+\sqrt{6}i$

Now solve the equation $\tt \: x=\frac{-2±2\sqrt{6}i}{2}$ when ± is minus. Subtract $\tt \: 2i\sqrt{6}$ from -2.

$\tt \: x=\frac{-2\sqrt{6}i-2}{2} \\ \\ \tt \: x=-\sqrt{6}i-1 \\ \\ \tt \: {{x=-1+\sqrt{6}i}}$

$\sf \: @WildCat7083$

Answer 2

Answer:

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