This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the quadratic equation \( x^2 - 5x + 6 = 0 \) using the quadratic formula, follow these steps: 1. Identify coefficients: In the equation \( ax^2 + bx + c = 0 \), we have: \( a = 1 \) \( b = -5 \) \( c = 6 \) 2. Quadratic formula: The quadratic formula is given by: \[ x = -b ± sqrt(b^2 - 4ac)2a \] 3. Calculate the discriminant: First, calculate \( b^2 - 4ac \): \[ b^2 - 4ac = (-5)^2 - 4(1)(6) = 25 - 24 = 1 \] 4. Substitute values into the formula: \[ x = -(-5) ± sqrt(1)2(1) = (5 ± 1)/(2) \] 5. Calculate the two possible values for \( x \): For \( x_1 \): \[ x_1 = (5 + 1)/(2) = (6)/(2) = 3 \] For \( x_2 \): \[ x_2 = (5 - 1)/(2) = (4)/(2) = 2 \] 6. Final solutions: The solutions to the equation \( x^2 - 5x + 6 = 0 \) are: \[ x = 3 and x = 2 \]