Solve (x − 3)² = 16
Quadratic equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = −1, x = 7 |
Step-by-step solution
6 steps-
1 Given\left(x - 3\right)^{2} = 16
Solve for x.
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2 Take the square root of both sides — remember both signs
A number and its negative give the same result when raised to an even power: 3² = 9 and (−3)² = 9. So if something squared equals k, that something is √k or −√k. Forgetting the minus sign loses a solution.
x - 3 = \pm 4 -
3 Split into two linear equationsx - 3 = 4\quad \text{or} \quad x - 3 = -4
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4 Add 3 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 = 7Move the constant terms to the right.
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5 Add 3 to both sidesx = -1
Move the constant terms to the right.
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6 Check\begin{aligned}x = -1:\quad 16 = 16\quad\checkmark\\ x = 7:\quad 16 = 16\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| −1 | 16 | 16 | ✓ |
| 7 | 16 | 16 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.