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Question
Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`
Solution
`4x^2 + 4bx −(a^2 − b^2 )= 0`
`x^2+bx-((a^2-b^2)/4)=0`
`x^2+2(b/2)x=(a^2-b^2)/4`
`x^2+2(b/2)x+(b/2)^2=(a^2-b^2)/4+(b/2)^2`
`(x+b/2)^2=a^2/4`
`x+b/2=+-a/2`
`x=-b/2+-a/2`
`x=(-b-a)/2,(-b+a)/2`
Hence, the roots are `(-b-a)/2 and (-b+a)/2 `
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