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
Step 1: Identify the quadratic equation from your work. Your work correctly simplified the equation to: y^2 - 4y - 13 = 0 Here, a=1, b=-4, and c=-13. Step 2: Apply the quadratic formula. The quadratic formula is y = -b ± sqrt(b^2 - 4ac)2a. Substitute the values of a, b, and c: y = -(-4) ± sqrt((-4)^2 - 4(1)(-13))2(1) y = 4 ± sqrt(16 - (-52))2 y = 4 ± sqrt(16 + 52)2 y = 4 ± sqrt(68)2 Step 3: Simplify the radical and the final expression. Simplify sqrt(68): sqrt(68) = sqrt(4 × 17) = 2sqrt(17) Substitute this back into the equation for y: y = 4 ± 2sqrt(17)2 Divide both terms in the numerator by 2: y = 2 ± sqrt(17) The final answers are y = 2 ± sqrt(17). That's 2 down. 3 left today — send the next one.