Final answer:
The quadratic equation 6x - 5 = x² is solved by putting it in standard form and using the quadratic formula, resulting in two solutions, x = 5 and x = 1.
Step-by-step explanation:
To solve the quadratic equation 6x - 5 = x² using the quadratic formula, we must first set the equation in standard form ax² + bx + c = 0. In this case, we subtract 6x and add 5 to both sides to get x² - 6x + 5 = 0.
The quadratic formula is given by x = (-b ± √(b² - 4ac))/(2a), where 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.
For our equation, a=1, b=-6, and c=5. Plugging these values into the quadratic formula, we obtain:
x = (6 ± √((-6)² - 4(1)(5)))/(2(1))
x = (6 ± √(36 - 20))/2
x = (6 ± √16)/2
x = (6 ± 4)/2
Therefore, there are two solutions:
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- x = (6 + 4)/2 = 5
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- x = (6 - 4)/2 = 1