Answer :
Answer:
x = 1.19258 and x = −4.19258
Step-by-step explanation:
The given equation is :
[tex]x^2+3x-5=0[/tex]
Keep x terms on the left and move the constant to the right side by adding it on both sides.
[tex]x^2+3x=5[/tex]
Take half of the x term and square it.
[tex](3\times \dfrac{1}{2})^2=\dfrac{9}{4}[/tex]
then add the result to both sides
[tex]x^2+3x+\dfrac{9}{4}=5+\dfrac{9}{4}\\\\(x+\dfrac{3}{2})^2=\dfrac{29}{4}\\\\(x+\dfrac{3}{2})=\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}+\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}-\sqrt{\dfrac{29}{4}}[/tex]
So,
x = 1.19258 and x = −4.19258
Hence, this is the required solution.