Answer:
x = 5 ± √46
Step-by-step explanation:
[tex]-x^2 + 10x + 21 = 0[/tex]
Take -1 common from L.H.S.
[tex]=> -1(x^2 -10x - 21) = 0[/tex]
Take -1 to R.H.S.
[tex]=> x^2 - 10x - 21 = 0[/tex]
Solve x using quadratic formula.
[tex]=> x = \frac{-(-10) + \sqrt{10^2 - 4 \times (-21) \times 1} }{2 \times 1} \: or \:\frac{-(-10) - \sqrt{10^2 - 4 \times (-21) \times 1} }{2 \times 1}[/tex]
[tex]=> x = \frac{10 + \sqrt{100 + 84} }{2} \: or \:\frac{10 - \sqrt{100 + 84} }{2}[/tex]
[tex]=> x = \frac{10 + \sqrt{184} }{2} \: or \: \frac{10-\sqrt{184} }{2}[/tex]
[tex]=> x = \frac{10 + 2\sqrt{46} }{2} \: or \: \frac{10 - 2\sqrt{46} }{2}[/tex]
[tex]=> x = (5 + \sqrt{46} ) \: or \: (5 - \sqrt{46} )[/tex]
