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finlep [7]
3 years ago
7

! + 3 − 5 = 0; by completing the square

Mathematics
1 answer:
mylen [45]3 years ago
6 0

Answer:

x = 1.19258 and x = −4.19258

Step-by-step explanation:

The given equation is :

x^2+3x-5=0

Keep x terms on the left and move  the constant to the right side  by adding it on both sides.

x^2+3x=5

Take half of the x term and square it.

(3\times \dfrac{1}{2})^2=\dfrac{9}{4}

then add the result to both sides

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}}

So,

x = 1.19258 and x = −4.19258

Hence, this is the required solution.

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