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If ax*x + bx +c = 0, then what is x?
ax^2+bx+c=0Complete the square, start by subtracting c from both sidesax^2 +bx = -cDivide by ax^2 +(b/a)x = -(c/a)add [(1/2)b/a)]^2 to both sides to produce a perfect square trinomial on the rightx^2 +(b/a)x + (b^2)/(4a^2)= (b^2)/(4a^2) - (c/a)Factor the left side(x+(b/(2a)))^2 = (b^2)/(4a^2) -(c/a)Get a common denominator on the right. (multiply -c/a by 4a/4a)(x+(b/(2a)))^2 = [b^2-4ac]/(4a^2)Take square root of both side (remember that square root yields a ± solution)√((x+(b/(2a)))^2) = ±√([b^2-4ac])/(4a^2))Simplify (√4a^2 = 2a)x+(b/2a) = ±√([b^2-4ac])/(2a)Solve for xx = -(b/2a) ±√([b^2-4ac])/(2a)x = [-b±√([b^2-4ac)]/(2a)
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