Question

(x-3)^2=25. (x+4)^2=9

Answer 1

(x-3)^2=25

(x-3)=5      (x-3)=-5

х=5+3=8      х=-5+3=-2

. (x+4)^2=9

(x+4)=3      (x+4)=-3

x=3-4=-1       x=-3-4=-7

Answer 2

To solve the equations, let's start by expanding the squared terms and then isolate the variable x.

1. (x - 3)^2 = 25

Expanding the squared term: (x - 3)(x - 3) = 25 x^2 - 3x - 3x + 9 = 25 x^2 - 6x + 9 = 25

Rearranging the equation: x^2 - 6x + 9 - 25 = 0 x^2 - 6x - 16 = 0

Now we can solve this quadratic equation. We can either factor it or use the quadratic formula.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -6, and c = -16. Plugging in the values: x = (-(-6) ± √((-6)^2 - 4(1)(-16))) / (2(1)) x = (6 ± √(36 + 64)) / 2 x = (6 ± √100) / 2 x = (6 ± 10) / 2

So we have two possible solutions: x1 = (6 + 10) / 2 = 16 / 2 = 8 x2 = (6 - 10) / 2 = -4 / 2 = -2

Therefore, the solutions for the first equation are x = 8 and x = -2.

2. (x + 4)^2 = 9

Expanding the squared term: (x + 4)(x + 4) = 9 x^2 + 4x + 4x + 16 = 9 x^2 + 8x + 16 = 9

Rearranging the equation: x^2 + 8x + 16 - 9 = 0 x^2 + 8x + 7 = 0

Now we can solve this quadratic equation.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 8, and c = 7. Plugging in the values: x = (-(8) ± √((8)^2 - 4(1)(7))) / (2(1)) x = (-8 ± √(64 - 28)) / 2 x = (-8 ± √36) / 2 x = (-8 ± 6) / 2

So we have two possible solutions: x1 = (-8 + 6) / 2 = -2 / 2 = -1 x2 = (-8 - 6) / 2 = -14 / 2 = -7

Therefore, the solutions for the second equation are x = -1 and x = -7.

In summary, the solutions for the given equations are: (x - 3)^2 = 25: x = 8 and x = -2

(x + 4)^2 = 9: x = -1 and x = -7