Math, asked by rianndsouza4, 1 year ago

Solve by factorisation method
(2x+3)square =16

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{\fcolorbox{red}{#ffdfff}{x = -7/2 or x = 1/2}}$

$\huge{\underline{\mathcal{\textcolor{red}{Step-by-step-explanation :}}}}$

$\huge{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

${(2x + 3)}^{2} = 16$

$\huge{\underline{\mathtt{\textcolor{green}{To \: \: Find :-}}}}$

Factors of the equation
Roots of the equation

$\huge{\underline{\mathtt{\textcolor{teal}{Concept \: \: used:-}}}}$

Factorisation of Polynomials

$\huge{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We have,

$\longmapsto$ ${(2x + 3)}^{2} = 16$

$\implies$ ${(2x)}^{2} + 2(2x)(3) + {(3)}^{2} = 16$

$\implies$ $4 {x}^{2} + 12x + 9 = 16$

$\implies$ $4 {x}^{2} + 12x + 9 - 16 = 0$

$\implies$ $4 {x}^{2} + 12x - 7 = 0$

$\implies$ $4 {x}^{2} + (14 - 2)x - 7 = 0$

$\implies$ $4 {x}^{2} + 14x - 2x - 7 = 0$

$\implies$ $2x(2x + 7) - 1(2x + 7) = 0$

$\implies$ $(2x + 7)(2x - 1) = 0$

$\implies$ $(2x + 7) = 0$ | $or \:$ $(2x - 1) = 0$

$\implies$ $2x = - 7 \: \: \: \: \: \: \:$ | $\implies$ $2x = 1$

$\implies$ $x =$ $\large{ - \frac{7}{2} \: \: \: \: }$ | $\implies$ $x =$ $\large{ \frac{1}{2} }$

$\huge{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$\large{x = - \frac{7}{2} }$

$\large{x = \frac{1}{2} }$

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Solve by factorisation method (2x+3)square =16

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Solve by factorisation method
(2x+3)square =16