Question

Solve for x: ax^2 =bx

Answer 1

0 or b/a

Explanation:

ax² = bx

Subtract bx from both sides:

ax² − bx = 0

Factor out x:

x (ax − b) = 0

x = 0

or

ax − b = 0

ax = b

x = b/a

Answer 2

x = 0 or b/a

Explanation:

ax² = bx

Subtract bx from each side

ax² - bx = 0

Factor the quadratic

x(ax - b) = 0

Apply the zero product rule

x = 0 ax - b = 0

ax = b

x = b/a

Check:

`\begin{array}{rclcrcl}a(0)^(2) & = & b(0) & \qquad & a\left ( (b)/(a) \right)^(2) & =&b \left ( (b)/(a)\right )\\\\0 & = & 0 & \qquad & (b^(2))/(a) & =&(b^(2))/(a)\\\\\end{array}`

OK.