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

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Solve `2x(x - 4) - 3(x + 5) = x(1 - x) - 16`  using the quadratic formula.

First simplify the expression.

`2x(x - 4) - 3(x + 5) = x(1 - x) - 16`

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

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

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

For this equation, a = 3, b = -12, and c = 1.

`(12+-sqrt(12^2 - 4(3)(1)))/(2*3)`

`(12+-sqrt(144-12))/6`

`(12 +-sqrt(132))/6` = `(12 +-2sqrt(33))/6` Cancel every term by 2.

`(6 +-sqrt(33))/3`

The solution using the quadratic formula is `(6 +-sqrt(33))/3`   or `x = 3.915, 0.085`

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To use the quadratic formula, we need to get the function into the form `ax^2 + bx + c = 0` We do that by completing the calculations of the original function. 

`2x(x-4)-3(x+5)=x(1-x)-16`
`2x^2-8x-3x-15=x-x^2-16` combine like terms

`2x^2-11x-15=-x^2+x-16 `

`3x^2-10x+1=0 `

`b=-10, a=3 c=1 x=(-b+-sqrt(b^2-4ac))/(2a)`

`(10+-sqrt(-10^2-4(3)(1)))/(2 xx 3)=(10+-sqrt(100-12))/6=`

`(10+-sqrt88)/6=10+-2sqrt(22)/6=(5+-sqrt22)/3`

`x~~3.23, 0.10`

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