5x^2 + 2x + 15 = 3x^2 + 13x + 27
We'll simplify this equation to make a quadratic equation of the form ax^2 + bx + c= 0
=> 5x^2 - 3x^2 + 2x - 13x + 15 - 27 = 0
=> 2x^2 - 11x - 12 = 0
For this equation, Discriminant (D) = (b^2 - 4ac) = -11^2 - 4(2)(-12) = 217.
Since d is not equal to 0, we won't be able to factorize 2x^2 - 11x - 12 by simply splitting the middle term. Using the quadratic formula is necessary.
Quadratic Formula: For ax^2 + bx + c = 0, x = {-b +- √(D)} / 2a
x = {-(-11) +- √217} / 2(2)
=> x =(11 +- √217) / 4
=> x = (11 + √217) / 4; x = (11 - √217) / 4
We'll simplify this equation to make a quadratic equation of the form ax^2 + bx + c= 0
=> 5x^2 - 3x^2 + 2x - 13x + 15 - 27 = 0
=> 2x^2 - 11x - 12 = 0
For this equation, Discriminant (D) = (b^2 - 4ac) = -11^2 - 4(2)(-12) = 217.
Since d is not equal to 0, we won't be able to factorize 2x^2 - 11x - 12 by simply splitting the middle term. Using the quadratic formula is necessary.
Quadratic Formula: For ax^2 + bx + c = 0, x = {-b +- √(D)} / 2a
x = {-(-11) +- √217} / 2(2)
=> x =(11 +- √217) / 4
=> x = (11 + √217) / 4; x = (11 - √217) / 4
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