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Question
Solve for x: `5/2 x^2 + 2/5 = 1 - 2x`.
Solution
Given, quadratic equation is `5/2 x^2 + 2/5 = 1 - 2x`
⇒ 25x2 + 4 = 10(1 – 2x)
⇒ 25x2 + 20x – 6 = 0
By using quadratic formula,
i.e., x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
Here, a = 25, b = 20 and c = –6
∴ x = `(-20 +- sqrt((20)^2 - 4(25)(-6)))/(2 xx 25)`
= `(-20 +- sqrt(400 + 600))/50`
= `(-20 +- 10sqrt(10))/50`
= `(-2 +- sqrt(10))/5`
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