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Solve for x in the equation 2x^2-5x+1=3 by completing the square.
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Nov 5, 2024
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Solve for x in the equation
by completing the square.
Mathematics
high-school
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2x^2 - 5x - 4 = 0
Next, divide all terms by 2 to make the coefficient of x^2 equal to one:
x^2 - (5/2)x - 2 = 0
The next step in completing the square involves adding and subtracting (b/2)^2 inside the parentheses. The b here refers to the coefficient of x, which is -(5/2). Therefore, (b/2)^2 is ((-5/4))^2 = 6.25.
Here's how it looks when we add and subtract this value:
x^2 - (5/2)x + (5/4)^2 - (5/4)^2 - 2 = 0
(x-(5/4))^2 - (5/4)^2 - 8 = 0
(x-(5/4))^2 = (5/4)^2 + 8
Now take the square root of both sides:
x-(5/4) = ± sqrt((25/16)+32)
x= (5±sqrt(537))/4
So, there are two solutions for x:
x= [(5+sqrt(537)) /8] and x= [(5-sqrt(537)) /8]
Mihe
answered
Nov 10, 2024
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Mihe
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