Solve 2x² = 8x
Quadratic equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = 0, x = 4 |
Step-by-step solution
8 steps-
1 Given2 x^{2} = 8 x
Solve for x.
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2 Move every term to the left side so the right side is 0
Factoring and the quadratic formula both work on an equation of the form … = 0. Subtracting the right side from both sides gets there without changing the solutions.
2 x^{2} - 8 x = 0 -
3 Divide both sides by the common factor 2
Every coefficient is divisible by 2. Dividing both sides by 2 gives smaller numbers and the same solutions, because 0 divided by 2 is still 0.
x^{2} - 4 x = 0 -
4 This is a quadratic in standard form ax² + bx + c = 0
Every quadratic equation can be arranged as ax² + bx + c = 0. Reading off a = 1, b = -4 and c = 0, signs included, shows which method fits: factoring, taking a square root or the quadratic formula.
a = 1,\quad b = -4,\quad c = 0 -
5 Every term contains x, so factor it out
Every term contains x, so x comes out as a common factor. Dividing both sides by x instead would be a mistake: it throws away the solution x = 0.
x \left(x - 4\right) = 0 -
6 Zero product property: a product is 0 only when one of its factors is 0
0 is the only number with this property: if a·b = 0, then a = 0 or b = 0. That is why the equation was first rearranged to … = 0 and factored: now each factor can be set to 0 on its own, giving a simpler equation for each.
x - 4 = 0\quad \text{or} \quad x = 0 -
7 Add 4 to both sides
An equation stays true as long as you do the same thing to both sides, like adding the same weight to both pans of a balance. Adding or subtracting the same amount on both sides moves a term to the other side, where it appears with the opposite sign.
x = 4Move the constant terms to the right.
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8 Check\begin{aligned}x = 0:\quad 0 = 0\quad\checkmark\\ x = 4:\quad 32 = 32\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 0 | 0 | 0 | ✓ |
| 4 | 32 | 32 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.