What are the solutions to the equation
(5x−15)
2
=−100?
If your question mean:
(5 x − 15 ) / 2 = - 100
then
Multiply both sides by 2
5 x - 15 = - 200
Add 15 to both sides
5 x - 15 + 15 = - 200 + 15
5 x = - 185
Divide both sides by 5
x = - 185 / 5
x = - 37
To find the solutions to the equation (5x−15)^2 = −100, we need to solve for x. Here's how you can do it:
Step 1: Expand the squared term:
(5x−15)^2 = (-100)
25x^2 - 150x + 225 = -100
Step 2: Move all the terms to one side of the equation:
25x^2 - 150x + 225 + 100 = 0
25x^2 - 150x + 325 = 0
Step 3: Simplify the equation if possible. In this case, we can divide all the terms by 25:
x^2 - 6x + 13 = 0
Step 4: Solve the quadratic equation. There are several methods to solve quadratic equations, including factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation x^2 - 6x + 13 = 0, the values of a, b, and c are:
a = 1, b = -6, c = 13
Plugging these values into the quadratic formula, we get:
x = (-(-6) ± √((-6)^2 - 4(1)(13))) / (2(1))
x = (6 ± √(36 - 52)) / 2
x = (6 ± √(-16)) / 2
Step 5: Simplify the square root:
x = (6 ± 4i) / 2
x = 3 ± 2i
Therefore, the solutions to the equation (5x−15)^2 = −100 are x = 3 + 2i and x = 3 - 2i, where i is the imaginary unit.