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
Welcome back ꧁❦❧ÅDË🥹💍ØLÅ🩷❦❧꧂ — missed you this week. Step 1: Expand the left side of the equation. The given equation is (y+3)(y-5) = 2y-2. Expand the product on the left side using the FOIL method (First, Outer, Inner, Last). (y+3)(y-5) = y · y + y · (-5) + 3 · y + 3 · (-5) y^2 - 5y + 3y - 15 y^2 - 2y - 15 Step 2: Rewrite the equation with the expanded term. y^2 - 2y - 15 = 2y - 2 Step 3: Move all terms to one side to form a standard quadratic equation ay^2 + by + c = 0. Subtract 2y from both sides: y^2 - 2y - 2y - 15 = -2 y^2 - 4y - 15 = -2 Add 2 to both sides: y^2 - 4y - 15 + 2 = 0 y^2 - 4y - 13 = 0 Step 4: Solve the quadratic equation using the quadratic formula. The quadratic formula is y = -b ± sqrt(b^2 - 4ac)2a. For the equation y^2 - 4y - 13 = 0, we have a=1, b=-4, and c=-13. Substitute these values into the formula: 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 5: Simplify the radical and the expression for y. Simplify sqrt(68): sqrt(68) = sqrt(4 × 17) = sqrt(4) × sqrt(17) = 2sqrt(17) Substitute this back into the expression for y: y = 4 ± 2sqrt(17)2 Divide both terms in the numerator by 2: y = (4)/(2) ± 2sqrt(17)2 y = 2 ± sqrt(17) The solutions are y = 2 + sqrt(17) and y = 2 - sqrt(17). The final answers are y = 2 ± sqrt(17). Send me the next one 📸