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 quadratic equation: Solve 3x^2 - 20 = 0 Step 1: Add 20 to both sides of the equation to isolate the term with x^2. 3x^2 = 20 Step 2: Divide both sides by 3 to isolate x^2. x^2 = (20)/(3) Step 3: Take the square root of both sides. Remember to include both the positive and negative roots. x = ±sqrt((20)/(3)) Step 4: Rationalize the denominator by multiplying the numerator and denominator by sqrt(3). x = ±sqrt(20)sqrt(3) × sqrt(3)sqrt(3) x = ±sqrt(20 × 3)3 x = ±sqrt(60)3 Step 5: Simplify the radical sqrt(60). Since 60 = 4 × 15, we have sqrt(60) = sqrt(4 × 15) = 2sqrt(15). x = ±2sqrt(15)3 The solutions are x = ±2sqrt(15)3. 3 done, 2 left today. You're making progress.