Step-by-step explanation:
1. x (x+ 5) = 2
Distribute x through the parenthesis;
x² + 5x = 2
Move the constant to the left-hand side and change it’s sign;
x² + 5x - 2 = 0
2. (s + 6)² = 15
Use (a + b)² = a² + 2ab + b²
s² + 12s + 36 = 15
s² + 12s + 36 -15 = 0
s² + 12s + 21 = 0
3. (x+8)(x+7)= 2
x² + 7x + 8x + 56 -2= 0
x² + 15x + 54 = 0
4.(x+2) (x-2)= 0
x² - 2x + 2x - 4 = 0
x² - 4 = 0
5. x² - 5x + 9x = - 16
x² + 4x + 16 = 0
6. (m² - 2)² + (m - 4)² = 15
m² - 4m + 4 + m² - 8m + 16= 15
2m² - 12 m + 20 - 15 = 0
2m² - 12m + 5 = 0
7. 3/a + 4/2a = a - 1
3/a + 2/a - a - 1 = 0
3 + 2 - a² + a/a
5 - a² + a/a
5 - a² + a= 0
-a² + a + 5 =0
-(-a² + a + 5)= 0
a² - a - 5 =0
8. 2w²/5 + 5w/4 = 10
8w² + 25w = 200
8w² + 25w - 200 = 0
9. 2/ x-1 + 4/x+5 = 7
2/x-1 + 4/x+5 - 7 = 0
2(x+5) + 4(x-1) - 7(x-1) (x+5)/(x-1)(x+5) = 0
2x+10+4x-4-7x²-35x+7x+35/(x-1)(x+5) = 0
-22x+10-4-7x²+35/(x-1)(x+5) =0
-22x+41-7x²/(x-1)(x-5) =0
-7x² - 22x + 41 = 0
7x² + 22x -41 = 0
10. 2/t - 3t/2 = 0
2/t - 3t/2 - 7 = 0
4 - 3t² - 14t/ 2t = 0
4 - 3t² - 14t = 0
-3t² - 14t + 4 = 0
3t² + 14t - 4 = 0
