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Use the Substitution Y= 2x +3 to Solve for X, If 4(2x+3)2 – (2x+3) – 14 =0. - ICSE Class 10 - Mathematics

Question

Use the substitution y= 2x +3 to solve for x, if 4(2x+3)2 – (2x+3) – 14 =0.

Solution

4(2x + 3) - (2x + 3) - 14 = 0

Put 2x + 3 = y

4y^2 - y - 14 = 0

=> 4y^2 - 8y + 7y - 14 = 0

=> 4y(y - 2) + 7(y - 2) = 0

if y - 2 = 0 or 4y + 7 = 0

then 2x = 3 -2 = 0 or 4(2x + 3) + 7 = 0

=> 2x = -1  or 8x = -19

=> x = (-1)/2 or x =(-19)/8

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Solution Use the Substitution Y= 2x +3 to Solve for X, If 4(2x+3)2 – (2x+3) – 14 =0. Concept: Quadratic Equations.
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