Q 30) x = -3 or x = 12.
Q 31) x = 1 or x = 2.
Q 32) x = -1/2 or x = 8.
Q 33) x = 2/5 or x = 3.
Q 34) x = 1.80424764151 or x = -0.5542476415.
Q 35) x = 1.5 or x = -1/3.
Step-by-step explanation:
Q 30)
x^2 - 9x - 36 = 0.
Solving by factoring:
Multiplying 1 and 36 yields 36. The factors whose difference results in 9 are 12 and 3. Therefore:
x^2 - 12x + 3x - 36 = 0.
x(x - 12) + 3(x - 12) = 0.
(x + 3)(x - 12) = 0.
Either x + 3 = 0 or x - 12 = 0.
Therefore, x = -3 or x = 12.
Q 31)
x^2 - 3x + 2 = 0.
Solving by factoring:
Multiplying 1 and 2 yields 2. The factors whose sum results in 3 are 2 and 1. Therefore:
x^2 - 2x - x + 2 = 0.
x(x - 2) - 1(x - 2) = 0.
(x - 1)(x - 2) = 0.
Either x - 1 = 0 or x - 2 = 0.
Therefore, x = 1 or x = 2.
Q 32)
2x^2 - 15x - 8 = 0.
Solving by factoring:
Multiplying 2 and 8 yields 16. The factors whose difference results in 15 are 16 and 1. Therefore:
2x^2 - 16x + x - 8 = 0.
2x(x - 8) + 1(x - 8) = 0.
(2x + 1)(x - 8) = 0.
Either 2x + 1 = 0 or x - 8 = 0.
Therefore, x = -1/2 or x = 8.
Q 33)
5x^2 - 17x + 6 = 0.
Solving by factoring:
Multiplying 5 and 6 yields 30. The factors whose sum results in 17 are 15 and 2. Therefore:
5x^2 - 15x - 2x + 6 = 0.
5x(x - 3) - 2(x - 3) = 0.
(5x - 2)(x - 3) = 0.
Either 5x - 2 = 0 or x - 3 = 0.
Therefore, x = 2/5 or x = 3.
Q 34)
4x^2 - 5x - 4 = 0.
Solving by completing the square:
4x^2 - 5x = 4.
x^2 - 5x/4 = 1.
(x)^2 - 2*(x)*(5/8) + (5/8)^2 = 1 + (5/8)^2.
(x - 5/8)^2 = 1 + 25/64.
(x - 5/8)^2 = 89/64.
x - 5/8 = ±1.17924764151.
x - 5/8 = 1.17924764151 or x - 5/8 = -1.17924764151.
Therefore, x = 1.80424764151 or x = -0.5542476415.
Q 35)
6x^2 - 7x - 3 = 0.
Solving by quadratic formula:
x = (-b ± √(b^2 - 4ac))/2a.
a = 6, b = -7, and c = -3.
x = (-(-7) ± √((-7)^2 - 4*(6)*(-3)))/2(6).
x = (7 ± √(49 + 72))/12.
x = (7 ± √(121))/12.
x = (7 ± 11)/12.
x = (7 + 11)/12 or x = (7 - 11)/12.
x = 18/12 or x = -4/12.
Therefore, x = 1.5 or x = -1/3.
In summary:
Q 30) x = -3 or x = 12!!!
Q 31) x = 1 or x = 2!!!
Q 32) x = -1/2 or x = 8!!!
Q 33) x = 2/5 or x = 3!!!
Q 34) x = 1.80424764151 or x = -0.5542476415!!!
Q 35) x = 1.5 or x = -1/3!!!
