Final answer:
To find the value of x in the equation 4x² - 23(92x) = 7, we can rearrange the equation into a quadratic equation and then use the quadratic formula to solve for x. After substituting the values into the formula and simplifying, we find that x can take on two possible values: 0 or 529.5.
Step-by-step explanation:
We can rearrange the equation to form a quadratic equation:
4x² - 23(92x) = 7
4x² - 2116x = 7
Now we can solve the quadratic equation by using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
For this equation, a = 4, b = -2116, and c = -7.
After substituting these values into the formula, we can solve for x:
x = (2116 ± sqrt((-2116)² - 4(4)(-7))) / (2(4))
Simplifying further:
x = (2116 ± sqrt(4467456 - (-112))) / 8
x = (2116 ± sqrt(4467568)) / 8
x = (2116 ± 2116) / 8
Now we have two possible values for x:
x = 0
or
x = 529.5