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Learn math step by step, from the basics

Short lessons where every question is solved step by step, with the intermediate calculations and the reason for each one.

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Quadratic equation

x2−5x+6=0x^2 - 5x + 6 = 0
  1. Δ=(−5)2−4⋅1⋅6\displaystyle \Delta = (-5)^2 - 4 \cdot 1 \cdot 6
  2. Δ=25−24=1\displaystyle \Delta = 25 - 24 = 1
  3. x=5±12\displaystyle x = \frac{5 \pm 1}{2}

Answer x1=2,  x2=3x_1 = 2,\; x_2 = 3

Percentage

15%⋅24015\% \cdot 240
  1. 10%⋅240=24\displaystyle 10\% \cdot 240 = 24
  2. 5%⋅240=12\displaystyle 5\% \cdot 240 = 12
  3. 24+12\displaystyle 24 + 12

Answer 3636

Fractions

23+14\frac{2}{3} + \frac{1}{4}
  1. lcm⁡(3,4)=12\displaystyle \operatorname{lcm}(3, 4) = 12
  2. 812+312\displaystyle \frac{8}{12} + \frac{3}{12}
  3. 8+312\displaystyle \frac{8 + 3}{12}

Answer 1112\frac{11}{12}

Rule of three

x12=4520\frac{x}{12} = \frac{45}{20}
  1. 20x=12⋅45\displaystyle 20x = 12 \cdot 45
  2. 20x=540\displaystyle 20x = 540
  3. x=54020\displaystyle x = \frac{540}{20}

Answer x=27x = 27

Logarithm

log⁡248−log⁡23\log_2 48 - \log_2 3
  1. log⁡2483\displaystyle \log_2 \frac{48}{3}
  2. log⁡216\displaystyle \log_2 16
  3. 16=24\displaystyle 16 = 2^4

Answer 44

What you get

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