1) x(x+3) = 1 Expanding the left side x^2 + 3x = 1 Subtracting 10 from both sides x^2 + 3x - 10 = Factoring the quadratic equation (x + 5)(x - 2) = Setting each factor to zero x + 5 = 0 or x - 2 = x = -5 or x = 2
2) x(x-1) = 4 Expanding the left side x^2 - x = 4 Subtracting 42 from both sides x^2 - x - 42 = Factoring the quadratic equation (x - 7)(x + 6) = Setting each factor to zero x - 7 = 0 or x + 6 = x = 7 or x = -6
3) (x+7)x = 1 Expanding the left side x^2 + 7x = 1 Subtracting 18 from both sides x^2 + 7x - 18 = Factoring the quadratic equation (x + 9)(x - 2) = Setting each factor to zero x + 9 = 0 or x - 2 = x = -9 or x = 2
4) (x-9)x = 3 Expanding the left side x^2 - 9x = 3 Subtracting 36 from both sides x^2 - 9x - 36 = Factoring the quadratic equation (x - 12)(x + 3) = Setting each factor to zero x - 12 = 0 or x + 3 = x = 12 or x = -3
1) x(x+3) = 1
Expanding the left side
x^2 + 3x = 1
Subtracting 10 from both sides
x^2 + 3x - 10 =
Factoring the quadratic equation
(x + 5)(x - 2) =
Setting each factor to zero
x + 5 = 0 or x - 2 =
x = -5 or x = 2
2) x(x-1) = 4
Expanding the left side
x^2 - x = 4
Subtracting 42 from both sides
x^2 - x - 42 =
Factoring the quadratic equation
(x - 7)(x + 6) =
Setting each factor to zero
x - 7 = 0 or x + 6 =
x = 7 or x = -6
3) (x+7)x = 1
Expanding the left side
x^2 + 7x = 1
Subtracting 18 from both sides
x^2 + 7x - 18 =
Factoring the quadratic equation
(x + 9)(x - 2) =
Setting each factor to zero
x + 9 = 0 or x - 2 =
x = -9 or x = 2
4) (x-9)x = 3
Expanding the left side
x^2 - 9x = 3
Subtracting 36 from both sides
x^2 - 9x - 36 =
Factoring the quadratic equation
(x - 12)(x + 3) =
Setting each factor to zero
x - 12 = 0 or x + 3 =
x = 12 or x = -3