Question

5x^2=4x+7 quadratic equations by square ​

Answer 1

GIVEN

An Equation 5x²=4x+7

To Find

The values of X by squaring method

Solution

5x²=4x-7

=>5x²-4x-7 (multiply by 5)

=>5(5x²-4x-7)

=>25x²-20x-35

=>(5x)²-2×5x×2+(2)²-(2)²-35

=>(5x-2)²-(2)²+35

=>(5x-2)²=4+35

$\implies 5x-2=\pm{\sqrt{39}}$

Taking as +

$\implies 5x={\sqrt{39}+2$

$\implies\:x=\frac{-{\sqrt{39}}+2}{5}$

Taking as -

$\implies\:x=\frac{{\sqrt{39}}-2}{5}$

Hence,the value of

$\boxed{\boxed{\sf\red{X=\frac{{\sqrt{39}}+2}{5},\frac{-{\sqrt{39}}+2}{5}}}}$

Answer 2

$\huge\underline{ \underline{ \bf{ \blue{ \: solution \: : = }}}} </p><p>$

by using quadratic formula,

$\bf {\boxed{\frac{ -b + - \sqrt{ {b }^{2} - 4ac} }{2a}}}$

⠀⠀⠀⟹⠀$x = \frac{ - ( - 4) + - \sqrt{ - 4 {}^{2} - 4 \times 5 \times ( - 7)} }{2 \times 5}$

⠀⠀⟹⠀⠀$x = \frac{ - 4 + - \sqrt{16 - 4 \times 5( - 7)} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{4 + - \sqrt{16 - 140} }{10}$

⠀⠀⠀⟹⠀⠀$x = \frac{4 + - \sqrt{156} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{4 + \times 2 \sqrt{39} }{10}$

⠀⠀⠀⠀⟹⠀⠀$x = \frac{2 \sqrt{39} + 4 }{10}$

⠀⠀⠀⟹⠀⠀${\bf{\boxed{\pink{x = \frac{ \sqrt{39} + 2}{ 5}}}}}$

⠀⠀⠀⠀⟹⠀$x = \frac{ - 4 - 2 \sqrt{39} }{10}$

⠀⠀⠀⠀⟹${\boxed{\pink{x = \frac{2 - \sqrt{39} }{5}}}}$