Solve this equation using the quadratic formula: 2x(x-4) - 3(x+5) = x(1-x) - 16

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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The quadratic formula is:`(-b+-sqrt(b^2-4ac))/(2a)`

Arrange the equation into the standard form of `ax^2 +bx+c`

`therefore 2x(x-4)-3(x+5)=x(1-x)-16` becomes (care with negative symbols)

`2x^2 - 8x - 3x -15=x-x^2 -16`

`therefore 2x^2+x^2-8x-3x-x-15+16=0` 


`3x^2 - 12x +1=0`

Now that we have the standard form,apply the formula where `a=3, b=-12 and c=1`

`therefore x= (-(-12) +- sqrt((-12)^2-(4(3)(1))))/(2(3))`

`therefore x= (12+-sqrt(144 - 12))/6`

`therefore x=(12+sqrt132)/6 and (12-sqrt132)/6`

`therefore x=(12+11.49)/6` `and (12-11.49)/6`

`therefore x=3.91 or ` `x=0.09`

or in surd form (simplify 132 to its prime bases of 2x2x11x3):

`x=2+(2sqrt33)/6` `or x=2-(2sqrt33)/6`

Ans"x=3.91 or x = 0.09


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