Solve x² − 81 = 0
Quadratic equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = 9, x = −9 |
Step-by-step solution
6 steps-
1 Givenx^{2} - 81 = 0
Solve for x.
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2 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 = 0 and c = -81, signs included, shows which method fits: factoring, taking a square root or the quadratic formula.
a = 1,\quad b = 0,\quad c = -81 -
3 There is no x term, so isolate x²x^{2} = 81
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4 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 = \pm 9 -
5 Solutionsx = 9\quad \text{or} \quad x = -9
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6 Check\begin{aligned}x = 9:\quad 0 = 0\quad\checkmark\\ x = -9:\quad 0 = 0\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 9 | 0 | 0 | ✓ |
| −9 | 0 | 0 | ✓ |
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