It's a supplementary material for Grade 9 Mathematics subject which provide parallel examples to the activities and quizzes on Grade 9 Math module in the Philippines.
There are several ways to solve quadratic equation. One of them is by completing the square.
Here is an example.
🤔 x² + 4x = 5
✏️Step 1. Get the coefficient of the linear term, 4x: 4
✏️Step 2. Divide 4 by 2: 2
✏️Step 3. Square the answer: 2²
✏️Step 4. Simplify: 4
✏️Step 5. Add the answer which is 4 on both sides of the equation: x² + 4x + 4 = 5 + 4 ( Info: Adding a number on both sides is called Addition Property of Equality)
✏️Step 6. Get the factor of the trinomial on the left side of the equation: (x+2) ( x+2) = 5 + 4
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Info: Look at the illustration above. The steps you undergo from the start is to get a square with side, x+2. Note that a square must have an equal value of the length and the width.
Thus, the steps above is to create a perfect square trinomial, x² + 4x + 4 which we can imagine as a square with side, x+2. That is what completing the square means.
✏️Step 7. Simplify the right side of the equation: (x+2) ( x+2) = 9
✏️Step 8. Get the square root on both sides of the equation: √(x+2)(x+2) = √9
✏️Step 9. It follows: x+2 = 3
(Note: √9 is +3 or -3, take only the positive root)
✏️Step 10. Add both sides by -2 to cancel out 2 from the left side of the equation. x+2-2 = 3-2
✏️Step 11. Simplify: x = 1
📖 Therefore, x = 1.
✏️Step 12. Look back. Very if the answer is correct by substituting x=1 into the quadratic equation x² + 4x = 5: 1² + 4(1) = 5 1 + 4 = 5 5 = 5 ✔️
So, the checking is done. ➖➖➖➖➖➖➖➖➖➖➖➖➖➖ 😎If you like it, hit the vote button below👇.
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