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# (x-1)(x+2)=70

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(x-1)(x+2)=70

(6x^2-7x)^2-2(6x^2-7x)-3=0

9(x-1)^2=4(x-2)^2

Sep 26, 2017

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(x - 1)(x + 2)  =  70

Multiply out the left side of the equation.

x2 + x - 2  =  70

Subtract  70  from both sides of the equation.

x2 + x - 72  =  0

Can you think of two numbers add to  1  and multiply to  -72?   →   -8  and  +9 .

So the left side can be factored like this...

(x - 8)(x + 9)  =  0           Now we set each factor equal to zero and solve for  x  .

x - 8  =  0      or      x + 9  =  0

x  =  8      or            x  =  -9

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I don't know the best way to do the second one, but I'm sure someone else on here does.

Here's the third one:

9(x - 1)2  =  4(x - 2)2     Take the ± square root of both sides.

(We only need to write the ± on one side though.)

$$\sqrt{9(x-1)^2}\,=\,\pm\sqrt{4(x-2)^2} \\~\\ \sqrt9\cdot\sqrt{(x-1)^2}\,=\,\pm\sqrt4\cdot\sqrt{(x-2)^2} \\~\\ 3(x-1)\,=\,\pm2(x-2)$$

$$3x-3\,=\,\pm(2x-4)$$       Split this into two seperate equations.

$$\begin{array} \ 3x-3=+(2x-4)\qquad\text{or}\qquad&3x-3=-(2x-4) \\~\\ 3x-3=2x-4&3x-3=-2x+4 \\~\\ x-3=-4&5x-3=4 \\~\\ x=-1&5x=7 \\~\\ &x=\frac75 \end{array}$$

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Sep 27, 2017