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-2x^2=-(5x+4) solve using the quadratic equation.

 May 31, 2019
 #1
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-2x2  =  -(5x + 4)

                               Distribute  -1  to the terms in parenthesees.

-2x2  =  -5x - 4

                               Add  2x2  to both sides of the equation.

0  =  2x2 - 5x - 4

 

2x2 - 5x - 4  =  0

 

2x2 + -5x + -4  =  0

 

This is a quadratic equation. We can use the quadratic formula to solve for  x .

 

The quadratic formula says that....

 

If     ax2 + bx + c  =  0     then     \( x=\frac{-\mathbf{\color{blue}b}\pm\sqrt{\mathbf{\color{blue}b}^2-4\mathbf{\color{Magenta}a}\mathbf{\color{Green}c}}}{2\mathbf{\color{Magenta}a}}\)

 

So...

 

Since     2x2 + -5x + -4  =  0     then     \( x=\frac{-(\mathbf{\color{blue}-5})\pm\sqrt{\mathbf{(\color{blue}-5})^2-4(\mathbf{\color{Magenta}2})(\mathbf{\color{Green}-4})}}{2(\mathbf{\color{Magenta}2})}\)

 

\(x=\frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-4)}}{2(2)}\\~\\ x=\frac{5\pm\sqrt{25+32}}{4}\\~\\ x=\frac{5\pm\sqrt{57}}{4}\\~\\ x=\frac{5+\sqrt{57}}{4}\qquad\text{or}\qquad x=\frac{5-\sqrt{57}}{4}\)

.
 May 31, 2019

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