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Completing square method : The standard form of quadratic equation is ax2 + bx + c = 0, where a ≠01) a$x^{2}$ + bx + c = 0 | 2x2+ 9x – 20 = 0 a = 2, b = 9 and c = -20 |
2) Divide by "a" on both sides $x^{2}$ + bx/ a + c/a = 0 |
Divide by "2" on both sides $x^{2}$ + 9x/ 2 -10 = 0 |
3) add - c on both sides $x^{2}$ + bx/a + c/a = 0 - c/a = –c /a ---------------------- $x^{2}$ + bx/a = -c/a |
add + 10 on both sides $x^{2}$ + 9x/2 - 10 = 0 +10 = –20 --------------------- $x^{2}$ + 9x/2 = 10 |
4) add $b^{2}$/ 4$a^{2}$on both sides $x^{2}$ + bx/a + $b^{2}$/ 4$a^{2}$ = - c/a + $b^{2}$/ 4$a^{2}$ |
add $9x^{2}$/4 x $2^{2}$= 81/16 $x^{2}$ + 9x/2 + 81/16 = 10 + 81/ 16 |
5) $(x + b/2a)^{2}= - c/a+ b^{2}/ 4a^{2}$ | $(x + 9/4)^{2}$ = (160 + 81)/16 |
6) $(x + b/2a)^{2} = (-4ac + b^{2})/ 4a^{2}$ | $(x + 9/4)^{2}$ = 241/16 |
7)$ (x + b/2a)^{2}=( b^{2} - 4ac)/4a^{2}$ | $(x + 9/4)^{2} $= 241/16 |
8) Taking square root on both sides (x + b/2a) =$\pm ( \sqrt(b^{2}$ - 4ac )/ 2a |
Taking square root on both sides (x + 9/4) = $\pm$ √241 /4 |
9)Add - b/2a on both sides x = - b/2a ± (√b2 - 4ac )/2a |
Add - 9/4 on both sides x = - 9/4 ± √241 /4 |
10) x = (- b ± √b2 - 4ac )/2a | x = (- 9 ± √241 )/ 4 |
Russia-Ukraine crisis update - 3rd Mar 2022
The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.