Illustrative Examples Solve each quadratic equation using the square root property. 4. 1. x² = 16 x = ± √√√16 x = +4 2. 2x² -144 = 0 x²-72=0 (Multiplication Property of Equality) x² = 72 (Addition Property of Equality) x = ± √√72 x= ± √36•2 = ±6√√2 X 3. 3x² -27=0 3x² = 27 (Addition Property of Equality) x² = 9 (Multiplication Property of Equality) x= ± √9 x=+3 (x²-1)-4 = 0 2 x² −1=4 x² = 3 x=± √√3 5. x² +1=0 x² = -1 = √-1 x = ti 6. (x+1)²-(x + 2)² = 0 (x+1)² = (x + 2)² x+1=x+2 .. No solution
Step-by-step explanation:
Your solutions are mostly correct, but there are a couple of errors:
4. x² = 16 is correct. However, when you take the square root, you should consider both the positive and negative square roots, so it's:
x = ± √16
x = ± 4
5. In this equation x² + 1 = 0, when you take the square root of -1, you'll get an imaginary number, not "ti." The correct answer is:
x² = -1
x = ± √(-1)
x = ±i (where "i" represents the imaginary unit)
6. In the last equation, (x+1)² = (x + 2)², you should consider both the positive and negative square roots when taking the square root of both sides, so it's:
x+1 = ±(x+2)
From here, you can solve for x. You'll get two solutions, not "no solution."