Do you know completing square method?

Question

Answer

Completing the square method is one of the methods to find the roots of the given quadratic equation.

Steps for Completing the square method

Suppose ax2 + bx + c = 0 is the given quadratic equation. Then follow the given steps to solve it by completing square method.

Write the equation in the form, such that c is on the right side.
If a is not equal to 1, then divide the complete equation by a, such that co-efficient of x2 is 1.
Now add the square of half of the co-efficient of term-x, (b/2a)2, on both the sides.
Factorize the left side of the equation as the square of the binomial term.
Take the square root on both the sides
Solve for variable x and find the roots..

Hope this will help you

Answer

Answer

**Completing the Square Method**

Completing the square is a mathematical technique used to manipulate quadratic equations in order to solve them or rewrite them in a more useful form. This method is particularly useful when we need to find the roots of a quadratic equation or when we want to convert a quadratic equation into its vertex form.

**Steps to Complete the Square:**

To complete the square, follow these steps:

1. **Write the quadratic equation in the standard form**: The standard form of a quadratic equation is given by ax² + bx + c = 0, where a, b, and c are constants.

2. **Isolate the x terms**: Move the constant term (c) to the right side of the equation, leaving only the x terms on the left side.

3. **Make the coefficient of x² equal to 1**: If the coefficient of x² (a) is not equal to 1, divide the entire equation by a to simplify it.

4. **Divide the coefficient of x by 2 and square it**: Take half of the coefficient of x (b) and square it. This value will be used in the next step.

5. **Add and subtract the value obtained in step 4 to the equation**: Add and subtract the value obtained in step 4 to both sides of the equation.

6. **Factor the perfect square trinomial**: On the left side of the equation, factor the perfect square trinomial obtained by combining the terms.

7. **Simplify the equation**: Simplify the equation by combining like terms.

8. **Solve for x**: Solve the equation by isolating x. If the equation is in the form (x - p)² = q, take the square root of both sides and solve for x.

9. **Check the solution**: Substitute the obtained value of x back into the original equation to ensure it satisfies the equation.

**Example:**

Let's say we have the quadratic equation x² + 6x + 5 = 0.

1. Write the equation in standard form: x² + 6x + 5 = 0.

2. Isolate the x terms: x² + 6x = -5.

3. Make the coefficient of x² equal to 1: Divide the equation by 1 to simplify it.

4. Divide the coefficient of x by 2 and square it: (6/2)² = 9.

5. Add and subtract the value obtained in step 4 to the equation: x² + 6x + 9 - 9 = -5.

6. Factor the perfect square trinomial: (x + 3)² - 9 = -5.

7. Simplify the equation: (x + 3)² - 9 + 5 = 0.

8. Solve for x: (x + 3)² - 4 = 0. Taking the square root of both sides, we get x + 3 = ±2.

9. Check the solution: Substitute x = -5 and x = -1 into the original equation to verify if they satisfy the equation.

Completing the square is a useful technique in solving quadratic equations and finding the vertex form of a quadratic equation. It allows us to manipulate and rewrite equations in a more manageable and useful form.

Similar Class 10 Doubts

Do any one know the easy way of completing squre method?

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Anyone explain me completing square method?

Find the roots of the following quadratic equations by the method of completing square method. 3xsquare 11x 10=0?

Find the roots of the following quadratic equations by the method of completing square method. 3x square plus 11x plus 10 =0?

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