Given:" "2x^2+8x-25=0 ....................Equation(1)
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color(blue)("Completing the square")
write as y=2(x^2+4x)-25=0
Introduce the correction k to compensate for the changes we are going to make. They introduce an error.
2(x^2+4x)-25+k=0 larr" at this stage "k=0
Take the power of 2 outside the brackets
2(x+4x)^2-25+k=0
Remove the x from 4x
2(x+4)^2-25+k=0
Halve the 4
2(x+2)^2-25+k=0............................. Equation(2)
From the part: color(red)(2)(xcolor(blue)(+2))^2 you get the constant color(red)(2)color(blue)(xx2)^2=8 which is the error.
so 8+k=0=> k=-8 Substituting into equation(2) gives
2(x+2)^2-25-8=0............................. Equation(2_a)
2(x+2)^2-33=0
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color(blue)("Determine "x_("intercepts"))
Write as(x+2)^2=33/2
Square root both sides
x+2=sqrt(33/2)
=>x=-2+-sqrt(33/2)
=> x~~-6.06 " and " 2.06 to 2 decimal places
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