Question

Answer 1

a) \(\left(2x-3\right)^2-49=0\)

\(\Leftrightarrow\left(2x-3\right)^2=49\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-3=7\\2x-3=-7\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

b) \(2x\left(x-5\right)-7\left(5-x\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(2x+7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{7}{2}\end{matrix}\right.\)

c) \(x^2-3x-10=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

Answer 2

\(a,\Leftrightarrow\left(2x-3-7\right)\left(2x-3+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}2x=10\\2x=-4\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\\ b,\Leftrightarrow\left(x-5\right)\left(2x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{7}{2}\end{matrix}\right.\\ c,\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

Answer 3

a. (2x - 3)² - 49 = 0

<=> (2x - 3)² = 7²

<=> 2x - 3 = 7

<=> 2x = 10

<=> x = 5

b. 2x(x - 5) - 7(5 - x) = 0

<=> 2x(x - 5) + 7(x - 5) = 0

<=> (2x + 7)(x - 5) = 0

<=> \(\left[{}\begin{matrix}2x+7=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3,5\\x=5\end{matrix}\right.\)

c. x² - 3x - 10 = 0

<=> x² - 5x + 2x - 10 = 0

<=> x(x - 5) + 2(x - 5) = 0

<=> (x + 2)(x - 5) = 0

<=> \(\left[{}\begin{matrix}x+2=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=5\end{matrix}\right.\)

Answer 4

a, \(\left(2x-3\right)^2-49=0\Leftrightarrow\left(2x-10\right)\left(2x+4\right)=0\Leftrightarrow x=5;x=-2\)

b, \(2x\left(x-5\right)-7\left(5-x\right)=0\Leftrightarrow\left(2x+7\right)\left(x-5\right)=0\Leftrightarrow x=-\dfrac{7}{2};x=5\)

c, \(x^2-3x-10=0\Leftrightarrow x^2+2x-5x-10=0\)

\(\Leftrightarrow x\left(x+2\right)-5\left(x+2\right)=0\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\Leftrightarrow x=-2;x=5\)

Answer 5

a. \(\left(3x-2\right)^2-49=0\)

\(\Leftrightarrow\left(2x-3-7\right)\left(2x-3+7\right)=0\)

\(\Leftrightarrow4\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

b. \(2x\left(x-5\right)-7\left(5-x\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(2x+7\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\2x+7=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-\dfrac{7}{2}\end{matrix}\right.\)

c. \(x^2-3x-10=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)