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
The problem involves solving a quadratic equation using the quadratic formula. Based on the student's work, the quadratic equation being solved is 3x^2 - 13x + 10 = 0. Step 1: Identify the coefficients of the quadratic equation. For ax^2 + bx + c = 0, we have a=3, b=-13, and c=10. Step 2: Apply the quadratic formula. The quadratic formula is given by: x = -b ± sqrt(b^2 - 4ac)2a Step 3: Substitute the values of a, b, and c into the formula. x = -(-13) ± sqrt((-13)^2 - 4(3)(10))2(3) Step 4: Simplify the expression. x = 13 ± sqrt(169 - 120)6 Step 5: Calculate the value under the square root. x = 13 ± sqrt(49)6 Step 6: Calculate the square root. x = (13 ± 7)/(6) Step 7: Calculate the two possible solutions for x. x_1 = (13 + 7)/(6) or x_2 = (13 - 7)/(6) Step 8: Simplify the solutions. x_1 = (20)/(6) or x_2 = (6)/(6) x_1 = (10)/(3) or x_2 = 1 The final answers are: x_1 = (10)/(3) or x_2 = 1