Question

[√2x+9] + x =13 find x

Answer 1

$\bold {\huge {Your~Solutions:-}}$


Q: [√2x+9] + x = 13
=> [√2x + 9] = x- 13
=> [√2x+9]² = (x - 13)²
=> 2x + 9 = (x - 13)²
=> 2x +9 = 169 + x² + 26x
=> x² - 28x + 160 = 0
=> x² - 20x - 8x + 160 = 0
=> x(x - 20) - 8(x-20) = 0
=> (x - 8) ( x - 20) = 0
=> x - 8 = 0 or x - 20 = 0
=> x = 8 or x = 20


Hope it helps you

Answer 2

$(\sqrt {2x + 9}) + x = 13\\\\ (\sqrt {2x +9}) = (13 - x)\\\\ \text{squaring both sides}\\\\(\sqrt {2x +9})^{2} = (13 - x)^{2}\\\\ 2x+9 = 13^{2} + x^{2} - 2\times 13\times x\\\\ 2x +9 =169 + x^{2} -26x\\\\ x^{2} - (26x+2x)+ (169-9) = 0\\\\ x^{2} - 28x + 160 =0\\\\ x^{2} -20x-8x+160 = 0\\\\ x(x-20)-8(x-20)=0\\\\(x-8)(x-20)=0\\\\ x-8 = 0\: or \: x-20 = 0 \\\\ x = 8 \: or \: 20$