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sukhopar [10]
3 years ago
10

Solve the following quadratic equation by completing the square ✓3x^2 + 10x + 7✓3 = 0​

Mathematics
1 answer:
solmaris [256]3 years ago
5 0

\sqrt{3}x^2+10x+7\sqrt{3}=0\\\\\sqrt3(x^2+\dfrac{10x}{\sqrt{3}}+7)=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+7=0\\\\x^2+\dfrac{10x}{\sqrt{3}}+\dfrac{25}{3}-\dfrac{25}{3} +7=0\\\\(x+\dfrac{5}{\sqrt{3}})^2 = \dfrac{4}{3}\\\\|x+\dfrac{5}{\sqrt{3}}| = \dfrac{2}{\sqrt{3}}\\\\x_1 =   \dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = -\dfrac{3}{\sqrt{3}} = -\sqrt{3}\\\\x_2 =    -\dfrac{2}{\sqrt{3}}-\dfrac{5}{\sqrt{3}} = \dfrac{-7}{\sqrt{3}} = -\dfrac{-7\sqrt{3}}{3}

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Answer:

\huge{ \boxed{ \bold{ \tt{14x + 14}}}}

Option E is the best choice.

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☯ Question : Simplify

  • 4 ( 3x + 2 ) + 2 ( x + 3 )

☯ Available options :

☐ 12x + 16

☐ 24x + 48

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✎ Step - by - step explanation :

  • \sf{4(3x + 2) + 2(x  + 3)}

Distribute 4 through the parentheses

\dashrightarrow{ \sf{12x + 8 + 2(x + 3)}}

Distribute 2 through the parentheses

\dashrightarrow{ \sf{12x + 8 + 2x + 6}}

Combine like terms. Only coefficients of like terms can be added or subtracted

\dashrightarrow{ \sf{12x + 2x + 8 + 6}}

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Add the numbers : 8 and 6

\dashrightarrow{ \boxed{ \sf{14x + 14}}}

Hope I helped!

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