Question

solve the following quadratic equation by completing squares method

m²-5m=-3
​

Answer 1

STEP

STEP1

STEP1:

STEP1:Trying to factor by splitting the middle term

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -5 .

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -5 . -3 + 1 = -2

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -5 . -3 + 1 = -2 -1 + 3 = 2

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -5 . -3 + 1 = -2 -1 + 3 = 2 Observation : No two such factors can be found !!

STEP1:Trying to factor by splitting the middle term 1.1 Factoring m2-5m-3 The first term is, m2 its coefficient is 1 .The middle term is, -5m its coefficient is -5 .The last term, "the constant", is -3 Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3 Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -5 . -3 + 1 = -2 -1 + 3 = 2 Observation : No two such factors can be found !!Conclusion : Trinomial can not be factored

Answer 2

$\huge\bold\orange{Solution}$

$\huge\boxed{\fcolorbox{purple}{ink}{ m²- 5 = - 3:}}$

$\huge\bold\orange{Standard \: form}$

$\huge\boxed{\fcolorbox{red}{ink}{ m²-5m+3=0 :}}$

$\small\boxed{\dag\sf\red{comparing \: m²-5m+3=0 \: with \: m²-2mn}\dag}$

$- 2mn = - 5m$

$n = \frac{5}{2} \\ {n}^{2} = \frac{24}{4}$

$m²-5m+ \frac{24}{4} \\\: is \: perfect \: square \: trinomial$

$\huge\boxed{\fcolorbox{red}{ink}{ m²-5m+3=0 :}}$

$\huge\fbox\pink{using-method✯}$

${m}^{2} - 5m + \frac{25}{4} - \frac{25}{4} + 3 = 0$

$(m- \frac{5}{2 } {)}^{2} - ( \frac{25}{4} - 3) = 0$

$(m- \frac{5}{2 } {)}^{2} - ( \frac{25 - 12}{4} ) = 0$

$(m - \frac{5}{2} {)}^{2} - ( \frac{13}{4}) = 0$

$( m - \frac{5}{2} {)}^{2} - ( \frac{ \sqrt{13} }{4} {)}^{2} = 0$

${(m - \frac{5}{2} + \frac{ \sqrt{13} }{2})(m - \frac{5}{2} - \frac{ \sqrt{13} }{2} ) = 0}$

$m - \frac{5}{2} + \frac{13}{2} = 0 \\ or \\ m - \frac{5}{2} - \frac{ \sqrt{13}}{2} = 0$

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

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

$\huge\ \: \pink{✯final \: Answer✯}$

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

are roots of given quadratic equation