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leonid [27]
3 years ago
6

If the quadratic formula is used to solve 2x(x + 5) = 4, what are the solutions? {-1/2, -9/2}

Mathematics
2 answers:
ankoles [38]3 years ago
7 0
X²+bx=c
x=[-b+√(b²+4c)]/2

2x(x+5)=4
2x²+10x=4
x²+5x=2

x=[-5+√(5²+4*4)]/2 

if b=-1/2 and c=-9/2
x= {1/2+√[(1/2)²+4*(-9/2)]}/2


PIT_PIT [208]3 years ago
5 0
<h2>Answer:</h2>

The solutions are:

           x=-5.372\ and\ x=0.372

<h2>Step-by-step explanation:</h2>

The equation is given by:

              2x(x+5)=4

on using the distributive property of multiplication in the left hand side of the equation we have:

2x\times x+2x\times 5=4\\\\i.e.\\\\2x^2+10x=4\\\\i.e.\\\\2x^2+10x-4=0\\\\i.e.\\\\2(x^2+5x-2)=0\\\\i.e.\\\\x^2+5x-2=0

Now, we know that the solution of the quadratic equation:

ax^2+bx+c=0 is given by:

x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}

Here we have:

a=1,\ b=5\ and\ c=-2

Hence, the solution is:

x=\dfrac{-5\pm \sqrt{5^2-4\times 1\times (-2)}}{2\times 1}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{25+8}}{2}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{33}}{2}\\\\x=\dfrac{-5+\sqrt{33}}{2},\ x=\dfrac{-5-\sqrt{33}}{2}

Hence, in decimal for the solution is:

x=-5.372\ and\ x=0.372

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