How to solve a quadratic equation?
A quadratic equation looks like this:
ax² + bx + c = 0
(where a, b, and c are numbers, and a is not zero)
To solve it, use this formula:
x = (-b ± √(b² - 4ac)) ÷ (2a)
Steps:
Find a, b, and c from your equation.
Calculate the discriminant: D = b² - 4ac
Check D:
If D > 0, there are two real answers
If D = 0, there is one real answer
If D < 0, answers are imaginary (complex numbers)
Plug values into the formula to get the answers for x.
Example: Solve 2x² + 3x - 2 = 0
a = 2, b = 3, c = -2
Calculate D = 3² - 4 × 2 × (-2) = 9 + 16 = 25
Since D > 0, two real answers
Find x:
x = (-3 ± √25) ÷ (2 × 2)
x = (-3 ± 5) ÷ 4
So,
x₁ = (-3 + 5) ÷ 4 = 2 ÷ 4 = 0.5
x₂ = (-3 - 5) ÷ 4 = -8 ÷ 4 = -2
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