Question

4x²+5x=7+4 find value of x.
Warning:- Random letter and wrong question not allowed.​

Answer 1

Answer:

$\boxed{\mathfrak{x = \frac{ - 5 \pm \sqrt{201} }{8}}}$

Explanation:

$\rm Solve \: for \: x \: over \: the \: real \: numbers: \\ \rm \implies4 x^2 + 5 x = 7 + 4 \\ \\ \rm 7 + 4 = 11: \\ \rm \implies 4 x^2 + 5 x = 11 \\ \\ \rm Divide \: both \: sides \: by \: 4: \\ \rm \implies x^2 + \frac{5x}{4} = \frac{11}{4} \\ \\ \rm Add \: \frac{25}{64} \: to \: both \: sides: \\ \rm \implies x^2 + \frac{5x}{4} + \frac{25}{64} = \frac{11}{4} + \frac{25}{64} \\ \\ \rm \implies x^2 + \frac{5x}{4} + \frac{25}{64} = + \frac{176 + 25}{64} \\ \\ \rm \implies x^2 + \frac{5x}{4} + \frac{25}{64} = \frac{201}{64} \\ \\ \rm Write \: the \: left \: hand \: side \: as \: a \: square: \\ \rm \implies {x}^{2} + \frac{5x}{8} + \frac{5x}{8} + \frac{25}{64} = \frac{201}{64} \\ \\ \rm \implies x(x + \frac{5}{8} ) + \frac{5}{8} (x + \frac{5}{8} ) = \frac{201}{64} \\ \\ \rm \implies (x + \frac{5}{8} ) (x + \frac{5}{8} ) = \frac{201}{64} \\ \\ \rm \implies {(x + \frac{5}{8} ) }^{2} = \frac{201}{64} \\ \\ \rm Take \: the \: square \: root \: of \: both \: sides: \\ \rm \implies \sqrt{{(x + \frac{5}{8} ) }^{2} } = \sqrt{\frac{201}{64}} \\ \\ \rm \implies x + \frac{5}{8} = \pm \frac{ \sqrt{201} }{8} \\ \\ \rm Subtract \: \frac{5}{8} \: from \: both \: sides: \\ \rm \implies x = - \frac{5}{8} \pm \frac{ \sqrt{201} }{8} \\ \\ \rm \implies x = \frac{ - 5 \pm \sqrt{201} }{8}$

Answer 2

$\rm 4x^2+5x=7+4$

$:\implies \rm 4x^2+5x=11$

$:\implies \rm 4x^2+5x-11=0$

Let's solve by completing the square method ,

$:\implies \rm \dfrac{4x^2+5x-11}{4}=\dfrac{0}{4}$

$:\implies \rm x^2+\dfrac{5x}{4}-\dfrac{11}{4}=0$

$:\implies \rm x^2+2.x.\dfrac{5}{8}-\dfrac{11}{4}=0$

$:\implies \rm x^2+2.x.\dfrac{5}{8}+\left(\dfrac{5}{8}\right)^2=\dfrac{11}{4}+\left(\dfrac{5}{8}\right)^2$

$:\implies \rm \left(x+\dfrac{5}{8}\right)^2=\dfrac{11}{4}+\dfrac{25}{64}$

$:\implies \rm x+\dfrac{5}{8}=\pm \sqrt{\dfrac{201}{64}}$

$:\implies \rm x+\dfrac{5}{8}=\pm \dfrac{\sqrt{201}}{8}$

$:\implies \bf x=\dfrac{-5\pm \sqrt{201}}{8}$