Solve 5x² = 45
Quadratic equation, worked out line by line the way a teacher would write it.
Answer
| Solutions | x = 3, x = −3 |
Step-by-step solution
8 steps-
1 Given5 x^{2} = 45
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.
5 x^{2} - 45 = 0 -
3 Divide both sides by the common factor 5
Every coefficient is divisible by 5. Dividing both sides by 5 gives smaller numbers and the same solutions, because 0 divided by 5 is still 0.
x^{2} - 9 = 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 = 0 and c = -9, signs included, shows which method fits: factoring, taking a square root or the quadratic formula.
a = 1,\quad b = 0,\quad c = -9 -
5 There is no x term, so isolate x²x^{2} = 9
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6 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 3 -
7 Solutionsx = 3\quad \text{or} \quad x = -3
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8 Check\begin{aligned}x = 3:\quad 45 = 45\quad\checkmark\\ x = -3:\quad 45 = 45\quad\checkmark\end{aligned}
Substituting each solution back makes both sides equal.
Check by substitution
| x | Left side | Right side | |
|---|---|---|---|
| 3 | 45 | 45 | ✓ |
| −3 | 45 | 45 | ✓ |
Change a number or try your own problem: the solver works it out the same way, with a graph and hint mode.