Question

10. Solve for all values of x algebraically (find the zeroes):
3x^2 +12x – 7 = x^2+ 3x – 2

Answer 1

x = -5 or 1/2

Explanation:

From the question,

3x²+12x-7 = x²+3x-2

Collect like terms

3x²-x²+12x-3x-7+2 = 0

2x²+9x-5 = 0

Using factorization method to solve the quadratic equation

2x²+10x-x-5 = 0

(2x²+10x)-(x+5) = 0

2x(x+5)-1(x+5) = 0

(x+5)(2x-1) = 0

Either,

x+5 = 0

x = -5

or,

2x-1 = 0

2x = 1

x = 1/2.

Therefore,

x = -5 or 1/2