Question

Solve the quadratic equation 2x ²78 +5=0 by completing the square method...

PLZZ help me ...

PLZZ solve this fast....
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=1\:and\:\frac{5}{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline\bold{Given :}} \\ \tt: \implies {2x}^{2} - 7x + 5 = 0 \\ \\ \red{\underline\bold{To \: Find :}} \\ \tt: \implies Value \: of \: x = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {2x}^{2} - 7x + 5 = 0 \\ \\ \tt \circ \: Dividing \: both \: side \: by \: 2 \\ \\ \tt: \implies \frac{ {2x}^{2} }{2} - \frac{7x}{2} + \frac{5}{2} = 0 \\ \\ \tt: \implies {x}^{2} - \frac{7x}{2} + \frac{5}{2} = 0 \\ \\ \tt \circ \: Both \: side \: adding \: (\frac{b}{2a})^{2} = (\frac{7}{2 \times 2} )^{2} = \frac{49}{16} \\ \\ \tt: \implies {x}^{2} - \frac{7x}{2} + \frac{49}{16} + \frac{5}{2} = \frac{49}{16} \\ \\ \tt: \implies ({x - \frac{7}{4} )}^{2} = \frac{49}{16} - \frac{5}{2} \\ \\ \tt: \implies {(x - \frac{7}{4} )}^{2} = \frac{49 - 40}{16} \\ \\ \tt: \implies ({x - \frac{7}{4}) }^{2} = \frac{9}{16} \\ \\ \tt: \implies x - \frac{7}{4} = \sqrt{ \frac{9}{16} } \\ \\ \tt: \implies x - \frac{7}{4} = \pm\frac{3}{4} \\ \\ \tt: \implies x = \pm\frac{3}{4} + \frac{7}{4} \\ \\ \tt: \implies x = \frac{7 \pm3}{4} \\ \\ \green{\tt: \implies x = 1 \: and \: \frac{5}{2} }$

Answer 2

2x^2-7x+5=0

Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :
x2-(7/2)x+(5/2) = 0

Subtract 5/2 from both side of the equation :
x2-(7/2)x = -5/2

x2-2(7/4)x = -5/2

x2-2(7/4)x +49/16= -5/2+49/16

(x-(7/4))^2 =( -40+49)/16

(x-(7/4))^2 = 9/16

(x-(7/4))^2 -9/16=0

(x-(7/4))^2 -(3/4)^2=0

(x-7/4-3/4) (x-7/4+3/4)=0

(x-10/4)(x-1)=0

x-10/4=0
x=10/4=5/2

x-1=0
x=1

Hopefully it’s helpful for you
Thanks