Solve for $x$ : $(x + 6) (x - 6) - {(x - 5)}^{2} = 40 - 17 (x - 2)$

4

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5

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Solution

The correct option is B $5$
Step 1. Simplify both
$(x + 6) (x - 6) - {(x - 5)}^{2} = 40 - 17 (x - 2)$
$\Rightarrow x^{2} - 36 - (x^{2} - 10 x + 25) = 40 - 17 x + 34 \Rightarrow x^{2} - 36 - x^{2} + 10 x - 25 = 40 - 17 x + 34$
$\Rightarrow 10 x + 17 x = 40 + 34 + 36 + 25$
$\Rightarrow 27 x = 135$
$\Rightarrow x = \frac{135}{27}$
$\Rightarrow x = 5$
Check : Putting $x = 5$
LHS $= (5 + 6) (5 - 6) - {(5 - 5)}^{2} = 11 \times (- 1) - 0 = - 11$
RHS $= 40 - 17 (5 - 2) = 40 - 17 \times 3 = 40 - 51 = - 11 =$ LHS
Hence, $x = 5$ .

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Solve for x: (x+6)(x−6)−(x−5)2=40−17(x−2)

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