Question

How many real solutions does the equation \displaystyle 4x^2-8x+10=-x^2-54x

Answer 1

2 real solutions

Step-by-step explanation

`4x^2-8x+10=-x^2-54x`

Step 1

reorder

`\begin{gathered} 4x^2-8x+10=-x^2-54x \\ 4x^2+x^2-8x+10+54x=0 \\ 5x^2+46x+10=0 \\ \end{gathered}`

Step 2

solve for x using the quadratic formula

`\begin{gathered} 5x^2+46x+10=0 \\ x=\frac{-b\pm\sqrt[]{b^2}-4ac}{2a} \\ \text{replace} \\ x=\frac{-46\pm\sqrt[]{46^2}-4\cdot5\cdot10}{2\cdot5} \\ x=\frac{-46\pm\sqrt[]{46^2}-200}{2\cdot5}=\frac{-46\pm\sqrt[]{1916}}{10} \\ Hence \\ \\ \frac{x_(1=)-46+\sqrt[]{1916}}{10} \\ x_2=\frac{-46\pm\sqrt[]{1916}}{10} \end{gathered}`

I hope this helps you