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Find all real solutions to the following equation

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Find all real solutions to the following equation 4x^2+x√2-1-0

asked Oct 6, 2018 in ALGEBRA 1 by anonymous

1 Answer

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The Equation

4x^2 + x√2 - 1  =  0

Compare it to quadratic form ax^2 + bx  =  0

a = 4, b = √2c = -1

Roots are  

x  =  [ - ± √(b^2 - 4ac) ] / 2a

x  =  { - √2 ± √[ (√2)^2 - 4(4)(-1) ] } / 2(4)

x  =  [ - √2 ± √(2 + 16) ] / 8

x  =  [ - √2 ± √[18 ] / 8

x  =  [ - √2 ± 3√2 ] / 8

 =  [ - √2 + 3√2 ] / 8       ;         =   [ - √2 - 3√2 ] / 8

 =  [ 2√2 ] / 8       ;         =   [ - 4√2 ] / 8

 =  √2 / 4       ;         =   - √2 ] / 2

Answer :

The Solutions are x  =  √2 / 4 and  =   - √2 ] / 2.

answered Oct 6, 2018 by homeworkhelp Mentor

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