x(x-3)+4= 3x^2 - 2(x+8)
3
To solve the equation x(x-3)+4= 3x^2 - 2(x+8), we need to simplify both sides of the equation and then find the value of x that makes the equation true.
Let's start by simplifying the left side of the equation:
x(x-3)+4 = 3x^2 - 2(x+8)
Using the distributive property on the left side, we get:
x*x + x*(-3) + 4 = 3x^2 - 2x - 2*8
Simplifying further:
x^2 - 3x + 4 = 3x^2 - 2x - 16
Next, we bring all the terms to one side of the equation to form a quadratic equation:
0 = 3x^2 - x^2 - 2x + 3x + 4 + 16
Combining like terms:
0 = 2x^2 + x - 20
Now we have a quadratic equation in standard form. To solve it, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing our equation with the standard form, we have:
a = 2
b = 1
c = -20
Substituting these values into the quadratic formula, we get:
x = (-1 ± √(1^2 - 4(2)(-20))) / (2(2))
Simplifying further:
x = (-1 ± √(1 + 160)) / 4
x = (-1 ± √161) / 4
Therefore, the solutions to the given equation are:
x = (-1 + √161) / 4
x = (-1 - √161) / 4
In summary, to solve the equation x(x-3)+4 = 3x^2 - 2(x+8), we simplified both sides of the equation, rearranged terms to form a quadratic equation, and then used the quadratic formula to find the solutions.