solve by completing the square method 3x²=15-4x ​

Question

solve by completing the square method 3x²=15-4x ​

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Khánh Gia 3 days 2021-07-20T04:38:17+00:00 2 Answers 3 views 0

Answers ( )

    0
    2021-07-20T04:39:21+00:00

    Answer:

    x = – 3, x = \frac{5}{3}

    Step-by-step explanation:

    Given

    3x² =15 – 4x ( add 4x to both sides )

    3x² + 4x = 15 ← factor out 3 from each term on the left side

    3(x² + \frac{4}{3} x) = 15

    To complete the square

    add/subtract ( half the coefficient of the x- term)² to x² + \frac{4}{3} x

    3(x² + 2(\frac{2}{3} )x + \frac{4}{9}\frac{4}{9} ) = 15

    3(x + \frac{2}{3} )² – \frac{4}{3} = 15 ( add \frac{4}{3} to both sides )

    3(x + \frac{2}{3} )² = 15 + \frac{4}{3} = \frac{49}{3} ( divide both sides by 3 )

    (x + \frac{2}{3} )² = \frac{49}{9} ( take the square root of both sides )

    x + \frac{2}{3} = ± \sqrt{\frac{49}{9} } = ± \frac{7}{3} ( subtract \frac{2}{3} from both sides )

    x = – \frac{2}{3} ± \frac{7}{3}, then

    x = – \frac{2}{3}\frac{7}{3} = – 3

    x = – \frac{2}{3} + \frac{7}{3} = \frac{5}{3}

    0
    2021-07-20T04:40:10+00:00

    Answer:

    Step-by-step explanation:

    3x²=15-4x

    divide by 3 on both sides

    x²=5-\frac{4}{3}x ​ ​

    move everything to one side

    x²+\frac{4}{3}x ​-5 = 0

    add the square of 1/2 the middle term of \frac{4}{3}  but also subtract it too

    x²+\frac{4}{3}x +( \frac{2}{3}  )^{2}​-5-( \frac{2}{3}  )^{2}​ = 0

    now use the property of a perfect square to rewrite

    (x+\frac{2}{3}) ^{2} -5 –\frac{4}{9} = 0

    rewrite 5 as a fraction

    (x+\frac{2}{3}) ^{2}\frac{45}{9}\frac{4}{9} = 0

    add up the fractions

    (x+\frac{2}{3}) ^{2}\frac{49}{9} = 0

    move to the other side

    (x+\frac{2}{3}) ^{2} = \frac{49}{9}

    take the square root of both sides 😛

    \sqrt{((x+\frac{2}{3}) ^{2} }  = \sqrt{\frac{49}{9} }

    much easier looking now, just use algebra to solve for x

    x + \frac{2}{3} = \frac{7}{3}

    subtract  \frac{2}{3}  from both sides

    x + \frac{2}{3} –  \frac{2}{3} = \frac{7}{3}\frac{2}{3}

    x = \frac{5}{3}

    🙂  

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