Question

How do I solve this equation and check the solutions?

Answer 1

SOLUTION :-

• By squaring on both sides :

$: \implies \sf {\big( \sqrt{20 - 8x} \:\big)}^{2} = x^2$

$:\implies \sf {20 - 8x} = {x}^{2}$

• Solving quadratic equation :

$: \implies\sf{ {x}^{2} + 8x - 20 = 0 }$

$: \implies\sf{ {x}^{2} + (10 - 2)x - 20 = 0 }$

$: \implies\sf{ {x}^{2} + 10x - 2x - 20 = 0 }$

$: \implies\sf{ x(x + 10) - 2(x + 10 )= 0 }$

$:\implies\sf{( x + 10 )(x - 2)= 0 }$

$: \implies\sf x + 10 = 0 \: or \: x - 2 = 0$

$: \implies\sf x = 0 - 10\: or \: x = 0 + 2$

$: \implies \underline{\boxed{ \bf{x = - 10 \: or \: x = 2}}}$

$\huge {\therefore}$ The roots of this equation are -10 and 2.

Answer 2

Answer:

1. x = -10
2. x = 2

I hope this helps!