Question

Use technology to solve for x.
2^x -5 = 3x - 6
What are the solutions?

Answer 1

x = 1 or

x = 1/2

Explanation:

2x² - 5 = 3x - 6

⇒ 2x² - 5 - 3x + 6 = 0

⇒ 2x² - 3x + 1 = 0

Using quadratinc formula, the roots are

`\frac{-b \pm\sqrt{b^(2) -4ac } }{2a}`

where, a = 2, b = -3 and c = 1

sub in the formula,

`\frac{-(-3) \pm\sqrt{(-3)^(2) -4(2)(1) } }{2(2)}\\\\= (3 \pm√(9 -8 ) )/(4)\\\\= (3 \pm√(1 ) )/(4)\\\\= (3 \pm 1 )/(4)\\\\= (3+1)/(4) \;or\; (3-1)/(4)\\ \\=(4)/(4) \; or\; (2)/(4) \\\\= 1 \; or \; (1)/(2)`