Question

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

Answer 1

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

Answer 2

Answer:

The solutions are:

           $x=-5.372\ and\ x=0.372$

Step-by-step explanation:

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:

$x=-5.372\ and\ x=0.372$