what value of x makes the following equation true? -5(x + 10)2=390,625
All work must be shown and explantions must be in complete sentences.
if im reading this correctly, youre multiplying (x+10) by -5 and 2, so distribute the numbers so you get -10x-100 and then add 100 to both sides and divide both sides by -10 to get your answer
again, I think they mean
-5(x + 10)^2=390,625
(why would you put a multiplier in front and behind a binomial ?)
(x+10)^2 = -78125
which is not possible since the square of anything is positive.
So, no solution.
To find the value of x that makes the equation true, we can follow these steps:
Step 1: Distribute the -5 to the terms inside the parentheses:
-5(x + 10)^2 = 390,625
-5 * (x + 10) * (x + 10) = 390,625
Step 2: Simplify the equation:
-5 * (x^2 + 20x + 100) = 390,625
-5x^2 - 100x - 500 = 390,625
Step 3: Move all the terms to one side of the equation to set it equal to zero:
-5x^2 - 100x - 890,625 = 0
Step 4: To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = -5, b = -100, and c = -890,625. Plugging in these values into the quadratic formula:
x = (-(-100) ± √((-100)^2 - 4(-5)(-890,625))) / (2 * -5)
x = (100 ± √(10,000 - 22,406,250)) / -10
x = (100 ± √(-22,396,250)) / -10
Step 5: Here, we encounter a problem. The discriminant (b^2 - 4ac) is negative, which means there are no real solutions for x. It implies that the equation -5(x + 10)^2 = 390,625 has no solution in the real number system.
Therefore, the equation has no value of x that makes it true.