Solve the following quadratic equation for x: 4x^2 + 4bx – (a^2 – b^2) = 0 - Algebra

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

Concept: Solutions of Quadratic Equations by Completing the Square
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