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frosja888 [35]
3 years ago
11

9x^2 + 24x + 20 = 4 Solve this by factoring. Thank you!

Mathematics
2 answers:
boyakko [2]3 years ago
3 0

Note that,

9x^2+24x+20=4\Longrightarrow9x^2+24x+16

Which factors to,

(3x+4)^2=0\Longrightarrow3x+4=0

And simplifies to <u>solution C</u>,

\boxed{x=-\dfrac{4}{3}}

Hope this helps.

Any additional questions please feel free to ask.

r3t40

rosijanka [135]3 years ago
3 0

Answer:

\large\boxed{C.\ x=-\dfrac{4}{3}}

Step-by-step explanation:

9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}

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For what values of $j$ does the equation $(2x+7)(x-5) = -43 + jx$ have exactly one real solution? express your answer as a list
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The values of 'j' are -11,5.

What is a Quadratic Equation?

  • Quadratic equations are the polynomial equations of degree 2 in one variable of the type f(x) = ax^{2} + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.
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Here, the given equation is (2x+7)(x-5) = - 43 + jx

On simplifying the equation we get,

2x^{2} -10x+7x-35=-43+jx\\2x^{2} -3x-35+43-jx=0\\2x^{2} -3x-jx+8=0\\2x^{2} -(3+j)x+8=0.....(1)\\

By comparing the given equation with the standard form of the quadratic equation we get,

a = 2

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Therefore,

(-(3+j))^{2} -4\times2\times8=0\\(3+j)^{2} -64=0\\(3+j)^{2} =64\\

Take the square root of both sides,

\sqrt{(3+j)^{2} }=\sqrt{64} \\

3 + j = ±8

Therefore,

3 + j = 8

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Hence, the possible values of 'j' are -11,5.

Learn more about the quadratic equation at brainly.com/question/8649555

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