Answer:
x=6+2√3 or x=6−2√3
Step-by-step explanation:
Let's solve your equation step-by-step by using completing the square.
5x^2−57x=3x−120
Step 1: Subtract 3x from both sides.
5x^2−57x−3x=3x−120−3x
5x^2−60x=−120
Step 2: Since the coefficient of 5x^2 is 5, divide both sides by 5.
5x2−60x/5
=
−120
/5
x2−12x=−24
Step 3: The coefficient of -12x is -12. Let b=-12.
Then we need to add (b/2)^2=36 to both sides to complete the square.
Add 36 to both sides.
x2−12x+36=−24+36
x2−12x+36=12
Step 4: Factor left side.
(x−6)2=12
Step 5: Take square root.
x−6=±√12
Step 6: Add 6 to both sides.
x−6+6=6±√12
x=6±√12
x=6+2√3 or x=6−2√3
