Final answer:
To find the value of x that makes the equation -4x(-3 + 5x) = -3(2x + 8) true, we can simplify both sides of the equation and solve the resulting quadratic equation. The values of x that make the equation true are x = -0.734 and x = 1.634.
Step-by-step explanation:
To find the value of x that makes the equation -4x(-3 + 5x) = -3(2x + 8) true, we can start by simplifying both sides of the equation.
Distribute the -4x and -3:
12x - 20x^2 = -6x - 24
Add like terms:
-20x^2 + 12x + 6x + 24 = 0
Combine like terms:
-20x^2 + 18x + 24 = 0
Now, we can solve this quadratic equation for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = -20, b = 18, and c = 24.
Substitute these values into the quadratic formula and simplify:
x = (-18 ± √(18^2 - 4(-20)(24)))/(2(-20))
Calculate the square root and simplify:
x = (-18 ± √(324 + 1920))/(-40)
x = (-18 ± √2244)/(-40)
x = (-18 ± 47.36)/(-40)
x = (-18 + 47.36)/(-40) or x = (-18 - 47.36)/(-40)
x = 29.36/(-40) or x = -65.36/(-40)
x = -0.734 or x = 1.634
Therefore, the two values of x that make the equation true are x = -0.734 and x = 1.634.