Mathematics: How do I solve this equation and check the solutions?

B) 1Step-by-step explanation:...

How do I solve this equation and check the solutions?

destinyshanece08

10.02.2022

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.

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