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