Question

m2-5m=-3 solve the qadratic equation by completing square method

Answer 1

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Answer 2

Answer:

$m=\frac{\sqrt{13+5}}{2},\frac{\sqrt{-13+5}}{2}$.

Step-by-step explanation:

Given : Quadratic equation $m^2-5m+3=0$

Solve : By completing method

Solution :

Quadratic general form is $ax^2+bx+c=0$

First divide the whole term with a to make coefficient of $x^{2}$ alone

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

Then Subtract and add the square and half of the coefficient of x to make the square.

Apply this in given quadratic equation,

$m^2-5m+3=0$

$m^2-5m+3+(\frac{5}{2})^2-(\frac{5}{2})^2=0$

$m^2-5m+(\frac{5}{2})^2=(\frac{5}{2})^2-3$

$(m-\frac{5}{2})^2=\frac{25}{4}-3$

$(m-\frac{5}{2})^2=\frac{13}{4}$

Taking root both side,

$m-\frac{5}{2}=\pm\sqrt{\frac{13}{4}}$

$m=\pm(\frac{\sqrt{13}}{2})+\frac{5}{2}$

$m=\frac{\sqrt{13}}{2}+\frac{5}{2},-\frac{\sqrt{13}}{2}+\frac{5}{2}$

$m=\frac{\sqrt{13+5}}{2},\frac{\sqrt{-13+5}}{2}$

Therefore, The solution of quadratic equation is $m=\frac{\sqrt{13+5}}{2},\frac{\sqrt{-13+5}}{2}$.