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Question
Solve the following equation by using quadratic equations for x and give your 5x(x + 2) = 3
Solution
5x(x + 2) = 3
⇒ 5x2 + 10x = 3
⇒ 5x2 + 10x - 3 = 0
Here a = 5, b = 10, c = -3
D = b2 - 4ac
= (10)2 - 4x 5 x (-3)
= 100 + 60
= 160
∴ x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
= `(10 ± sqrt(160))/(2 xx 5)`
= `(-10 ± sqrt(16 xx 10))/(10)`
= `(-10 ±4sqrt(10))/(10)`
= `(-10 ± 4(3.162))/(10)`
= `(-10 ± 12.648)/(10)`
∴ x1 = `(-10 + 12.648)/(10)`
= `(2.648)/(10)`
= 0.2648
x2 = `(-10 - 12.648)/(10)`
= `(-22.648)/(10)`
= -2.2648
∴ x = 0.26, -2.26.
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