hi i need to solve this question but i don't know how to do it when there is dividing included
x(x-8):5=92
i did this much and then i found out that what i was doing was wrong
x(x-8):5*5=92*5
2x-8=460
2x=468
x=234
but it seems wrong
To solve the equation x(x-8)/5 = 92, you need to simplify and isolate the variable x. Here's the correct step-by-step approach:
1. Start by distributing x to both terms inside the parentheses:
(x^2 - 8x)/5 = 92
2. Multiply both sides of the equation by 5 to eliminate the fraction:
5 * (x^2 - 8x)/5 = 92 * 5
x^2 - 8x = 460
3. Rearrange the equation into a quadratic equation by moving all terms to one side, resulting in:
x^2 - 8x - 460 = 0
4. To solve this quadratic equation, you have a couple of options. You can either factor it, complete the square, or use the quadratic formula. Let's use the quadratic formula here:
x = (-b ± √(b^2 - 4ac))/(2a)
For our equation x^2 - 8x - 460 = 0:
a = 1, b = -8, c = -460
Plugging these values into the quadratic formula, we get:
x = (-(-8) ± √((-8)^2 - 4 * 1 * (-460)))/(2 * 1)
x = (8 ± √(64 + 1840))/2
x = (8 ± √(1904))/2
x = (8 ± 43.64)/2
5. Solve for x by using both the positive and negative roots:
x = (8 + 43.64)/2 = 51.64/2 = 25.82
x = (8 - 43.64)/2 = -35.64/2 = -17.82
Therefore, the solutions to the equation x(x-8)/5 = 92 are x ≈ 25.82 and x ≈ -17.82.