Question

Which equation has the same solution as x^2-10x-3=5?

Answer 1

Explanation:

To find the equation that has the same solution as x^2 - 10x - 3 = 5, we can start by simplifying the left side of the equation by adding 8 to both sides:

x^2 - 10x - 3 = 5

x^2 - 10x - 8 = 0

Now we need to find an equation with the same solutions as this simplified equation. We can do this by factoring the quadratic equation into two linear factors:

x^2 - 10x - 8 = 0

(x - 2)(x - 8) = 0

Therefore, the solutions to the equation x^2 - 10x - 3 = 5 are x = 2 and x = 8. We can write two equations that have these solutions:

(x - 2) = 0

(x - 8) = 0

So the two equations that have the same solution as x^2 - 10x - 3 = 5 are x - 2 = 0 and x - 8 = 0. These equations can be simplified as x = 2 and x = 8, which are the same solutions as the original quadratic equation. Therefore, the equations x - 2 = 0 and x - 8 = 0 have the same solution as x^2 - 10x - 3 = 5.

Answer 2

(x - 5)^2 = 33

Explanation:

Add 3 to both sides

• x^2 - 10x - 3 = 5

Simplify

• x^2 - 10x = 8

Calculate the "magic number":

• b = -10 → b/2 = -5 → (b/2)^2 = 25

Add the magic number to both sides

• x^2 -10x + 25 = 8 + 25

Factor left side

• (x - 5)(x - 5) = 33

Rewrite left side as a perfect square

• (x - 5)^2 = 33

Solution

(x - 5)^2 = 33