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
Here is the solution to the equation: 20) Solve 5y^2 + 8y - 100 = y^2 + 4y - 37 Step 1: Move all terms to one side of the equation to set it equal to zero. 5y^2 - y^2 + 8y - 4y - 100 + 37 = 0 Step 2: Combine like terms. 4y^2 + 4y - 63 = 0 Step 3: Use the quadratic formula y = -b ± sqrt(b^2 - 4ac)2a to solve for y. Here, a=4, b=4, and c=-63. y = -4 ± sqrt(4^2 - 4(4)(-63))2(4) y = -4 ± sqrt(16 + 1008)8 y = -4 ± sqrt(1024)8 Step 4: Calculate the square root. sqrt(1024) = 32 Step 5: Substitute the value back into the formula and find the two possible solutions for y. y = (-4 ± 32)/(8) For the first solution: y_1 = (-4 + 32)/(8) = (28)/(8) = (7)/(2) For the second solution: y_2 = (-4 - 32)/(8) = (-36)/(8) = -(9)/(2) The solutions are: y = (7)/(2), y = -(9)/(2)