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Question #d2d79

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Jul 29, 2017

$x = 65 + \sqrt{2125} = 111.1$ $x = 65+sqrt2125 = 111.1$

$x = 65 - \sqrt{2125} = 18.9$ $x= 65-sqrt2125 =18.9$

Explanation:

You have got to the step of $1425 = (125 - x) (x - 5)$ $1425 = (125-x)(x-5)$

Now get rid of the brackets, and you will end up with an $x^{2}$ $x^2$ term.
That means it is a quadratic equation.

Make it equal to $0$ $0$ and then decide on an appropriate method of solving..

$\times \times \times \times \times \times x 1425 = (125 - x) (x - 5)$ $color(white)(xxxxxxxxxxxxx)1425 = (125-x)(x-5)$

$\times \times \times \times \times \times x 1425 = 125 x - 625 - x^{2} + 5 x$ $color(white)(xxxxxxxxxxxxx)1425 = 125x-625 -x^2 +5x$

$x^{2} - 130 x + 625 + 1475 = 0$ $x^2 -130x +625 + 1475 =0$

$\times \times x x^{2} - 130 x + 2100 = 0$ $color(white)(xxxxx) x^2-130x +2100 =0$

Complete the square:

$x^{2} - 130 x \times \times = - 2100 \leftarrow {(\frac{- 160}{2})}^{2} = 65^{2}$ $x^2 -130x color(white)(xxxx) = -2100" "larr ((-160)/2)^2 = 65^2$

$x^{2} - 130 x + 65^{2} = - 2100 + 65^{2}$ $x^2 -130x +65^2 = -2100 +65^2$

${(x - 65)}^{2} = 2, 125$ $(x-65)^2 = 2,125$

$x - 65 = \pm \sqrt{2125}$ $x-65 = +-sqrt2125$

$x = 65 + \sqrt{2125} = 111.1$ $x = 65+sqrt2125 = 111.1$

$x = 65 - \sqrt{2125} = 18.9$ $x= 65-sqrt2125 =18.9$

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