Solve `2.7x^2-3.8x-6`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to solve for x the quadratic equation `2.7x^2 - 3.8x - 6 = 0` , hence, you may try convert the decimal coeficients into fractions, such that:

(27/10)x^2 - (38/10)x - 6 = 0 => 27x^2 - 38x - 60 = 0

 

You need to use quadratic formula to find the solutions to equation, such that:

`x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)`

Identifying the coefficients a,b,c yields:

`a = 27, b = -38, c = -60`

`x_(1,2) = (38 +- sqrt((-38)^2 - 4*27*(-60)))/(2*27)`

`x_(1,2) = (38 +- sqrt(7924))/54 => x_1 = (38+89.01)/54 => x_1 = 2.35`

`x_2 = (38-89.01)/54 => x_2 = -0.94`

Hence, evaluating the solutions to the given quadratic equation, using quadratic formula, yields

`x_1 = 2.35, x_2 = -0.94. `

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oldnick | (Level 1) Valedictorian

Posted on

`2.7x^2-3.8x-6=0`

first multiply it by 10:

 

`27x^2-38x-60=0`

 

`Delta=(-38)^2-4(27)(-60)=1444+6480=7924>0`

Equation has two real different solutions:

`x=(38+-sqrt(7924))/54=(38+-2sqrt(1981))/54=(19+-sqrt(1981))/27=`

`x_1=-0.944756`    `x_2=2.352164`

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