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The first part of this question requires be student to realise that touching the x axis equates to f(x) equalling 0, so we must equate the expression to 0.

Next we need to factorise the expression....

5(2c - 3) = 19

5x2c - 5x3 = 19

10c - 15 = 19

10c = 19 + 15

10c = 34

c = 34/10 = 3.4

Pythagoras' Theorem: a² + b² = c²     where a, b, c relate to the sides of a right-angled triangle, and c is the hypoteneuse.

Use the equation to find the length on...

x =3 or x= -3

First, I would make sure the pupil understands why rationalising fractions is necessary. Then I would acquaint them with the relevant vocabulary so they can express their thought process better...