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andriy [413]
1 year ago
13

PLEASE HELP. DON’T NEED DEEP EXPLANATION JUST ANSWERS.

Mathematics
1 answer:
vladimir2022 [97]1 year ago
7 0

Answer:

\large {\textsf{B and E}}\ \implies x_1=-2\sqrt{5}-3,\ x_2=+2\sqrt{5}-3

Step-by-step explanation:

<u>Quadratic Formula:</u> x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

<u>Quadratic Equation:</u> ax² + bx + x = 0, where a ≠ 0

<u>Given equation:</u> x² + 6x + 9 = 20

<u>Step 1:</u> Subtract 20 from both sides.

x² + 6x + 9 - 20 = 20 - 20

⇒ x² + 6x - 11 = 0

<u>Step 2:</u> Identify the values of <em>a</em>, <em>b</em>, and <em>c</em> and substitute them in the formula.

⇒ a = 1, b = 6, c = -11

x=\dfrac{-6\pm\sqrt{\bold{6^2}-4(1)(-11)}}{\bold{2(1)}}\\\\x=\dfrac{-6\pm\sqrt{36\bold{\ - \ 4(-11)}}}{2}\\\\x=\dfrac{-6\pm\sqrt{\bold{36+44}}}{2}\\\\x=\dfrac{-6\pm\sqrt{80}}{2}\\\\x=\dfrac{-6\pm\sqrt{16\times5}}{2}\implies \dfrac{-6\pm\sqrt{\bold{16}}\times\sqrt{5}}{2} \\\\x=\dfrac{-6\pm4\sqrt{5}}{2}

<u>Step 3:</u> Separate into possible cases.

x_1=\dfrac{-6-4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{-4\sqrt{5}}{2}\implies \boxed{-3-2\sqrt{5}\ \ \textsf{or}\ -2\sqrt{5}-3}\\\\x_2=\dfrac{-6+4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{4\sqrt{5}}{2}\implies \boxed{-3+2\sqrt{5}\ \ \textsf{or}\ \ 2\sqrt{5}-3}

Learn more about quadratic equations here:

brainly.com/question/27988045

brainly.com/question/27031173

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