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|1|{sbBox2-problem} 2+|Solve the quadratic equation: \$4x^2 + 8x + 14 = 0\$. |2|{sbBox2-step}|Simplify the equation|\$2(2x^2 + 4x + 7) = 0\$

\$2x^2 + 4x + 7 = 0\$ |3|{sbBox2-formula}|To solve the quadratic equation \$2x^2 + 4x + 7 = 0\$, we can use the quadratic formula. The quadratic formula states that for an equation in the form \$ax^2 + bx + c = 0\$, the solutions for x can be found using the formula|\$x = (-b ± \sqrt (b^2 - 4ac)) / (2a)\$ |4|{sbBox2-hint}|For the equation \$2x^2 + 4x + 7 = 0\$ then, substituting these values into the quadratic formula, we get|a = 2, b = 4, and c = 7

\$x = (- 4 ± \sqrt (4^2 - 4 times 2 times 7)) / (2 times 2)\$

\$x = (- 4 ± \sqrt (- 40)) / 4\$ |5|{sbBox2-step}|After simplification|\$x = (- 4 ± \sqrt (2^2 i^2 5)) / 4\$

\$x = (- 4 ± 2i \sqrt 5) / 4\$

\$x = (- 2 ± i \sqrt 5) / 2\$ |6|{sbBox2-step}|This gives us two possible solutions|\$x_1 = (- 2 + i \sqrt 5) / 2\$ and \$x_2 = (- 2 - i \sqrt 5) / 2 \$ |7|{sbBox2-answer}| Option | A Unresolved directive in comm4/a4Steps206.adoc - include::{sbComm4-path-lesson1}/tableFooterSteps.adoc[]

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