Solve the following quadratic using completing the square.

1. ײ - 2×=2


2. ײ - 4× - 21=0


3. ײ + 10ײ + 9=0


4. ײ + 14×=23


5. ײ - 10×= -17

Answer:Let's solve each quadratic equation using the method of completing the square:1. For the equation \(x^2 - 2x = 2\):- Move 2 to the other side: \(x^2 - 2x - 2 = 0\).- To complete the square, take half of the coefficient of \(x\), which is \(-1\), and square it: \((-1)^2 = 1\).- Add and subtract 1 inside the equation:  \(x^2 - 2x + 1 = 2 + 1\)- Simplify:  \((x - 1)^2 = 3\)- Take the square root of both sides:  \(x - 1 = \pm \sqrt{3}\)- Solve for \(x\):  \(x = 1 \pm \sqrt{3}\)2. For the equation \(x^2 - 4x - 21=0\):- Move -21 to the other side: \(x^2 - 4x = 21\).- Half of \(-4\) is \(-2\), square it to get 4.- Add and subtract 4:  \(x^2 - 4x + 4 = 21 + 4\)- Simplify:  \((x - 2)^2 = 25\)- Take the square root:  \(x - 2 = \pm5\)- Solve for \(x\):  \(x = 2 \pm5\)- Solutions are: \(x=7\) and \(x=-3\).3. For the equation \(x^2 +10 x^2 +9=0\), note that it appears to have a typo because it combines two quadratic terms. Assuming it was intended as a quadratic in one variable, please clarify.4. For the equation \(x^2 +14 x=23\):- Move 23 to the other side:   \(x^2 +14 x -23=0\).- Half of 14 is 7; square it to get 49.- Add and subtract this inside the equation:   \(x^2 +14 x +49=23+49\)- Simplify:   \((x+7)^2=72\)- Take the square root:   \(x+7=\pm\sqrt{72}\) or simplified as \(x+7=\pm6\sqrt{2}\)- Solve for x:   \(x=-7 ±6√2\)5. For the equation \(x^2 -10 x= -17\):- Move -17 to the other side:   \(x^2 -10 x +17=0\).- Half of -10 is -5; square it to get25.- Add and subtract25:   \(x^2 -10 x +25=17+25\)- Simplify:   (x−5)^2=42- Take square root:x−5=±√42−5±√42These are the solutions for each quadratic using completing the square method. Please verify any typos or clarify if needed.Step-by-step explanation:

Answered by rosezysoledad | 2025-08-18