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: Expand both sides of the equation. The left side is (x+5)^2, which expands to x^2 + 2(x)(5) + 5^2. The right side is 7(x-5), which expands to 7x - 7(5). x^2 + 10x + 25 = 7x - 35 Step 2: Move all terms to one side to form a quadratic equation in the standard form ax^2 + bx + c = 0. Subtract 7x from both sides and add 35 to both sides. x^2 + 10x - 7x + 25 + 35 = 0 x^2 + 3x + 60 = 0 Step 3: Solve the quadratic equation using the quadratic formula x = -b ± sqrt(b^2 - 4ac)2a. For the equation x^2 + 3x + 60 = 0, we have a=1, b=3, and c=60. x = -(3) ± sqrt((3)^2 - 4(1)(60))2(1) x = -3 ± sqrt(9 - 240)2 x = -3 ± sqrt(-231)2 Step 4: Simplify the expression involving the square root of a negative number. Since the discriminant = -231 is negative, the solutions will be complex numbers. We can write sqrt(-231) as isqrt(231), where i = sqrt(-1). x = -3 ± isqrt(231)2 The solutions are: x_1 = -3 + isqrt(231)2 x_2 = -3 - isqrt(231)2 The final answer is x = -3 ± isqrt(231)2. Send me the next one 📸